180 degrees The sum of the three angles of any triangle is equal to 180 degrees.
Contents
 1 Is a triangle 180 or 360?
 2 Do all triangle add up to 180 degrees?
 3 Does a 90 degree triangle add up to 180?
 4 Is a triangle 270 degrees?
 5 Do all 4 sided shapes have 360 degrees?
 6 Is a triangle 1 2 3 possible?
 7 What are the 3 angles of a triangle?
Is a triangle 180 or 360?
A – The three interior angles of a triangle will always have a sum of \(180°\). A triangle cannot have an individual angle measure of \(180°\), because then the other two angles would not exist \((180°+0°+0°)\). The three angles of a triangle need to combine to \(180°\).
Do all triangle add up to 180 degrees?
The sum of the interior angle measures of a triangle always adds up to 180°.
Does a 90 degree triangle add up to 180?
How to find an angle in a right triangle – Basic Geometry Find angle C. Possible Answers: Explanation : First, know that all the angles in a triangle add up to 180 degrees. Each triangle has 3 angles. Thus, we have the sum of three angles as shown: where we have angles A, B, and C. In our right triangle, one angle is 25 degree and we’ll call that angle A. The other known angle is 90 degrees and we’ll call this angle B. Thus, we have Simplify and solve for C. Which of the following can be two angle measures of a right triangle? Possible Answers: Correct answer: Explanation :
 A right triangle cannot have an obtuse angle; this eliminates the choice of 100 and 10.
 The acute angles of a right triangle must total 90 degrees. Three choices can be eliminated by this criterion:
 The remaining choice is correct:
A right triangle has an angle that is 15 more than twice the other. What is the smaller angle? Possible Answers: Correct answer: Explanation : The sum of the angles in a triangle is 180. A right triangle has one angle of 90. Thus, the sum of the other two angles will be 90.
 Let = first angle and = second angle
 So the equation to solve becomes or
 Thus, the first angle is and the second angle is,
 So the smaller angle is
Angle in the triangle shown below (not to scale) is 35 degrees. What is angle ? Possible Answers: degrees degrees degrees degrees Correct answer: degrees Explanation : The interior angles of a triangle always add up to 180 degrees. We are given angle and since this is indicated to be a right triangle we know angle is equal to 90 degrees.
Thus we know 2 of the 3 and can determine the third angle. Angle is equal to 55 degrees. Which of the following cannot be true of a right triangle? Possible Answers: A right triangle can be equilateral. The measures of the angles of a right triangle can total, One leg can be longer than the hypotenuse.
A right triangle can have an obtuse angle. None of the other statements can be true of a right triangle. Correct answer: None of the other statements can be true of a right triangle. Explanation :
 All of these statements are false.
 A right triangle can be equilateral.
 False: An equilateral triangle must have three angles that measure each.
 One leg can be longer than the hypotenuse.
 False: Each leg is shorter than the hypotenuse.
 A right triangle can have an obtuse angle.
 False: Both angles of a right triangle that are not right must be acute.
 The measures of the angles of a right triangle can total,
 False: The measures of any triangle total,
In triangle, what is the measure of angle ? Possible Answers: Correct answer: Explanation : The formula to find all the angles of a triangle is: To solve for the measure of angle, we plug in the values of and, Since angle is a right angle, we know the measure will be, Find the degree measure of the missing angle. Possible Answers: Correct answer: Explanation :
 All the angles in a triangle add up to 180 º.
 T o find the value of the remaining angle, subtract the known angles from 180º:
 Therefore, the third angle measures 43 º,
The right triangle has two equal angles, what is each of their measures? Possible Answers: Correct answer: Explanation :
 The internal angles of a triangle always add up to 180 degrees, and it was given that the triangle was right, meaning that one of the angles measures 90 degrees.
 This leaves 90 degrees to split evenly between the two remaining angles as was shown in the question.
 Therefore, each of the two equal angles has a measure of 45 degrees.
What is the missing angle in this right triangle? Possible Answers: Correct answer: Explanation :
 The angles of a triangle all add up to,
 This means that,
 Using the fact that 90 is half of 180, we can figure out that the missing angle, x, plus 34 adds to the remaining 90, and we can just subtract
Solve for : Possible Answers: Correct answer: Explanation : The angles of a triangle add together to 180 degrees. We already know that one of the angles is 90 degrees, so we can subtract 90 from 180: the other 2 angles have to add to 90 degrees. We can now subtract to get x: Jhanvi Certified Tutor Pandit Deendayal Petroleum University, Bachelor of Science, Information Technology.
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Is a triangle 270 degrees?
ESO Supernova According to Albert Einstein, the threedimensional fabric of space can be curved. In a flat Universe (or on a flat surface), Euclidean geometry applies: the inner angles of a rectangle add up to 360 degrees and those of a triangle add up to 180 degrees. : ESO Supernova
Why is a triangle not 360?
Why do triangles have 180 degrees? – Which brings us to the main question for today: Why is it that the interior angles of a triangle always add up to 180 0 ? As it turns out, you can figure this out by thinking about the interior and exterior angles of a triangle.
 To see what I mean, either grab your imagination or a sheet of paper because it’s time for a little mathematical artsandcrafts drawing project.
 Start by drawing a right triangle with one horizontal leg, one vertical leg, and with the hypotenuse extending from the top left to the bottom right.
 Now make a copy of this triangle, rotate it around 180 0, and nestle it up hypotenusetohypotenuse with the original (just as we did when figuring out opens in a new window how to find the area of a triangle ).
Finally, make yet another copy of the original triangle and shift it to the right so that it’s sitting right next to the newlyformed rectangle. With me so far? If so, your picture should look like this: What’s the point of this picture? Take a look at the interior angle at the bottom right of the original triangle (the one labeled “A”). Now take a look at the two angles that make up the exterior angle for that corner of the triangle (the ones labeled “B” and “C”).
 As we know, if we add up the interior and exterior angles of one corner of a triangle, we always get 180 0,
 And our little drawing shows that the exterior angle in question is equal to the sum of the other two angles in the triangle.
 In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the angle in the bottom right corner to make a 180 0 angle.
RELATED: opens in a new window The World of Trigonometry For the sake of simplicity, we’ve made our drawing using a right triangle. But it turns out that you can make an exactly analogous drawing using any triangle you fancy, and you’ll always end up reaching the same conclusion. The inevitable conclusion of this game is that the interior angles of a triangle must always add up to 180 0, Our lovely and elegant little drawing proves that this must be so. Or does it?
Can a triangle equal 360?
Angles on a straight line equal 180 degrees. Adding the three exterior angles or multiplying 120 by three gives us 360 degrees. Therefore, the sum of the measures of the exterior angles of an equilateral triangle are 360 degrees. This fact is also true for any triangle.
Why is triangle 180?
One exterior angle of a triangle is equal to the sum of the other two angles in the triangle. The exterior angle is obtained by extending the side of the triangle. Since it is a straight line, the angle is 180 °.
Do all angles add up to 360?
The four angles in any quadrilateral always add to 360 360°, but there are a few key properties of quadrilaterals that can help us calculate other angles.
What angle is 45 degree?
A 45degree angle is an acute angle. It is half of the right angle or a 90degree angle.
Is a triangle always 90 degrees?
A triangle can have at most one right angle, or an angle that has a measure of 90°. When a triangle has a right angle, it is called a right triangle. In general, all triangles are either a right triangle, or they are not a right triangle. Therefore, a triangle can have either one right angle or no right angles.
What angles add to 180?
Supplementary Angles Supplementary angles are two whose measures add up to 180 °, The two angles of a, like ∠ 1 and ∠ 2 in the figure below, are always supplementary. But, two angles need not be adjacent to be supplementary. In the next figure, ∠ 3 and ∠ 4 are supplementary, because their measures add to 180 °, Example 1: Two angles are supplementary. If the measure of the angle is twice the measure of the other, find the measure of each angle.
 Let the measure of one of the supplementary angles be a,
 Measure of the other angle is 2 times a,
 So, measure of the other angle is 2 a,
 If the sum of the measures of two angles is 180 °, then the angles are supplementary.
 So, a + 2 a = 180 °
 Simplify.
 3 a = 180 °
 To isolate a, divide both sides of the equation by 3,
 3 a 3 = 180 ° 3 a = 60 °
 The measure of the second angle is,
 2 a = 2 × 60 ° = 120 °
 So, the measures of the two supplementary angles are 60 ° and 120 °,
 Example 2:
 Find m ∠ P and m ∠ Q if ∠ P and ∠ Q are supplementary, m ∠ P = 2 x + 15, and m ∠ Q = 5 x − 38,
 The sum of the measures of two supplementary angles is 180 °,
 So, m ∠ P + m ∠ Q = 180 °
 Substitute 2 x + 15 for m ∠ P and 5 x − 38 for m ∠ Q,
 2 x + 15 + 5 x − 38 = 180 °
 Combine the like terms. We get:
 7 x − 23 = 180 °
 Add 23 to both the sides. We get:
 7 x = 203 °
 Divide both the sides by 7,
 7 x 7 = 203 ° 7
 Simplify.
 x = 29 °
 To find m ∠ P, substitute 29 for x in 2 x + 15,
 2 ( 29 ) + 15 = 58 + 15
 Simplify.
 58 + 15 = 73
 So, m ∠ P = 73 °,
 To find m ∠ Q, substitute 29 for x in 5 x − 38,
 5 ( 29 ) − 38 = 145 − 38
 Simplify.
 145 − 38 = 107
 So, m ∠ Q = 107 °,
See also, : Supplementary Angles
Which angle is 180 degree?
The 180degree angle is called a straight angle.
What is a 135 degree triangle called?
An angle measuring 135° is an obtuse angle.
What is a 270 to 360 angle called?
The correct option is A reflex. If an angle is greater than 180∘ and less than 360∘, then it is called a reflex angle. Hence, 270∘ is a reflex angle. Suggest Corrections.3.
What is 270 to sin?
FAQs on Sin 270 Degrees Sin 270 degrees is the value of sine trigonometric function for an angle equal to 270 degrees. The value of sin 270° is 1.
Why don’t triangles exist?
There’s No Such Thing as Triangles
 “I’m frightened and I cannot sleep,” the little child said. “I fear there might be triangles
 underneath my bed.”
“There might be ghosts,” the mother mused. “I cannot speak to those. There may be ghouls and goblins who will nibble on your toes. There could be longtoothed monsters with their eyes a gleaming red. But there’s no such thing as triangles!
 They’re only in your head.”
Teaching math is a weird job. I’m paid to tell children about imaginary things. To be sure, no one mistakes me for J.K. Rowling or J.R.R. Tolkien; there are no slowtalking trees, giant spiders, or unionized cleaning elves in my line of work. I traffic in things much stranger than that, and much less beloved.
Things like quadratic equations and noninvertible matrices. Things so abstract that—by definition— they cannot exist in the physical world. The official story, the party line, is that mathematics is essential for everyone, as indispensable for modern life as comfy jeans and good facesoap. But honestly! I mean, how much algebra do you use in your typical week? Unless you’re a relationship counselor for x ‘s and y ‘s, it’s probably not much.
What’s cool about math isn’t that it’s “useful.” It’s that math walks the coastline between reality and imagination, between discovery and invention. And precisely when math is furthest from reality, that’s when it offers the best views of reality—like a mountaintop overlooking a valley.
I’m not just talking about sophisticated, obscure stuff like the “inverse hyperbolic tangent” or the “convex hull of a set.” I’m talking about all mathematics, even the most elemental, familiar stuff. I’m talking, in fact, about triangles. Witness the triangle, a fond old friend. This humble twodimensional figure is, by all accounts, one of realest and most tangible objects in all of mathematics.
Ever since you were little, you’ve seen triangles everywhere. You find them in jacko’lantern eyes, corporate logos, and grilled cheese sandwiches halved diagonally. They crop up in all kinds of construction projects: the pyramids, the supports beneath the Golden Gate Bridge, the tracks of roller coasters.
 When architects and engineers want a shape that’s sturdy and dependable, they turn to the triangle.
 There’s only one problem.
 Triangles don’t exist.
 I don’t mean to alarm you, and I hope I’m not spoiling any fond childhood memories of geometric forms.
 But triangles are like Santa Claus, the tooth fairy, and Beyoncé: too strange and perfect to exist in the actual world.
By definition, a triangle is a twodimensional figure ( perfectly flat ) with three sides ( perfectly straight ) meeting at three vertices ( perfectly sharp ). Under this standard, every shape we’ve mentioned, from roller coaster struts to corporate logos, is utterly and hopelessly flawed.
 They meet none of the criteria.
 Sure, they may look compellingly perfect from a distance, like celebrities you’ve never met.
 But get to know them better.
 Start zooming in.
 See those imperfections emerge: the minor wobble in the “straight” side, the tiny round to the “sharp” corner, the slight thickness to this supposedly “flat” shape? These aren’t just coincidental features, flaws in our manufacturing process.
They’re inescapable. No physical “triangle” can ever be totally perfect. The closer you look, the more it will dissolve into jagged pixels, until—by the time you reach the level of atoms and quarks—the triangle looks nothing like its idealized geometric reputation.
There’s no such thing as triangles. There are only jumbles of matter in faintly trianglelike arrangements. You’ve never met a real triangle, and neither have I. We’ve encountered only cheap approximations, dancing shadows, sorry knockoff versions of the true and perfect original. Triangles, as understood by every mathematician in the world, are mere abstractions.
Works of geometric fiction. Their story is not a biography; it’s a fantasy novel. And yet they’re so darn useful, This is the maddening paradox at the heart of mathematics. Every mathematical object is much like the triangle: inspired by reality, but idealized beyond any physical existence.
 In the words of Ian Stewart, mathematics “hovers uneasily between the real and the notreal.
 Eugenia Cheng says that math studies not “real things” but rather “the ideas of things.” And G.H.
 Hardy once boasted, “‘Imaginary’ universes are so much more beautiful than this stupidly constructed ‘real’ one.” By the account of its own highest practitioners, mathematics is an absurdly theoretical and impractical discipline.
And yet it is how we make buildings stand and spaceships fly. Math is deliberately useless, and that’s what makes it so useful. : There’s No Such Thing as Triangles
Which triangle Cannot exist?
From Wikipedia, the free encyclopedia The Penrose triangle, also known as the Penrose tribar, the impossible tribar, or the impossible triangle, is a triangular impossible object, an optical illusion consisting of an object which can be depicted in a perspective drawing, but cannot exist as a solid object.
 It was first created by the Swedish artist Oscar Reutersvärd in 1934.
 Independently from Reutersvärd, the triangle was devised and popularized in the 1950s by psychiatrist Lionel Penrose and his son, prominent Nobel Prizewinning mathematician Sir Roger Penrose, who described it as “impossibility in its purest form”.
It is featured prominently in the works of artist M.C. Escher, whose earlier depictions of impossible objects partly inspired it.
Do all 4 sided shapes have 360 degrees?
Quadrilaterals
 Quadrilaterals
 Learning Objective(s)
 · Identify properties, including angle measurements, of quadrilaterals.
are a special type of polygon. As with triangles and other polygons, quadrilaterals have special properties and can be classified by characteristics of their angles and sides. Understanding the properties of different quadrilaterals can help you in solving problems that involve this type of polygon.
Picking apart the name “quadrilateral” helps you understand what it refers to. The prefix “quad” means “four,” and “lateral” is derived from the Latin word for “side.” So a quadrilateral is a foursided polygon. Since it is a, you know that it is a twodimensional figure made up of straight sides. A quadrilateral also has four angles formed by its four sides.
Below are some examples of quadrilaterals. Notice that each figure has four straight sides and four angles. Interior Angles of a Quadrilateral The sum of the interior angles of any quadrilateral is 360°. Consider the two examples below. You could draw many quadrilaterals such as these and carefully measure the four angles. You would find that for every quadrilateral, the sum of the interior angles will always be 360°. You can also use your knowledge of triangles as a way to understand why the sum of the interior angles of any quadrilateral is 360°. These measurements add up to 180º. Now look at the measurements for the other triangles—they also add up to 180º! Since the sum of the interior angles of any triangle is 180° and there are two triangles in a quadrilateral, the sum of the angles for each quadrilateral is 360°. Specific Types of Quadrilaterals Let’s start by examining the group of quadrilaterals that have two pairs of parallel sides. These quadrilaterals are called They take a variety of shapes, but one classic example is shown below. Imagine extending the pairs of opposite sides. They would never intersect because they are parallel. Notice, also, that the opposite angles of a parallelogram are congruent, as are the opposite sides. (Remember that “congruent” means “the same size.”) The geometric symbol for congruent is, so you can write and,
The parallel sides are also the same length: and, These relationships are true for all parallelograms. There are two special cases of parallelograms that will be familiar to you from your earliest experiences with geometric shapes. The first special case is called a, By definition, a rectangle is a parallelogram because its pairs of opposite sides are parallel.
A rectangle also has the special characteristic that all of its angles are right angles; all four of its angles are congruent. The other special case of a parallelogram is a special type of rectangle, a, A square is one of the most basic geometric shapes. It is a special case of a parallelogram that has four congruent sides and four right angles. A square is also a rectangle because it has two sets of parallel sides and four right angles. A square is also a parallelogram because its opposite sides are parallel. So, a square can be classified in any of these three ways, with “parallelogram” being the least specific description and “square,” the most descriptive. In summary, all squares are rectangles, but not all rectangles are squares. All rectangles are parallelograms, but not all parallelograms are rectangles. And all of these shapes are quadrilaterals. The diagram below illustrates the relationship between the different types of quadrilaterals. You can use the properties of parallelograms to solve problems. Consider the example that follows.
Example  
Problem  Determine the measures of and,  
is opposite is opposite  Identify opposite angles.  
A property of parallelograms is that opposite angles are congruent.  
= 60°, so = 60° = 120°, so = 120°  Use the given angle measurements to determine measures of opposite angles.  
Answer  = 60° and = 120° 
There is another special type of quadrilateral. This quadrilateral has the property of having only one pair of opposite sides that are parallel. Here is one example of a, Notice that, and that and are not parallel. You can easily imagine that if you extended sides and, they would intersect above the figure.
If the nonparallel sides of a trapezoid are congruent, the trapezoid is called an, Like the similarly named triangle that has two sides of equal length, the isosceles trapezoid has a pair of opposite sides of equal length. The other pair of opposite sides is parallel. Below is an example of an isosceles trapezoid.
In this trapezoid ABCD, and,
A) Some trapezoids are parallelograms. Incorrect. Trapezoids have only one pair of parallel sides; parallelograms have two pairs of parallel sides. A trapezoid can never be a parallelogram. The correct answer is that all trapezoids are quadrilaterals. B) All trapezoids are quadrilaterals. Correct. Trapezoids are foursided polygons, so they are all quadrilaterals. C) All rectangles are squares. Incorrect. Some rectangles may be squares, but not all rectangles have four congruent sides. All squares are rectangles however. The correct answer is that all trapezoids are quadrilaterals. D) A shape cannot be a parallelogram and a quadrilateral. Incorrect. All parallelograms are quadrilaterals, so if it is a parallelogram, it is also a quadrilateral. The correct answer is that all trapezoids are quadrilaterals. 
You can use the properties of quadrilaterals to solve problems involving trapezoids. Consider the example below.
Example  
Problem  Find the measure of,  
= 360°  The sum of the measures of the interior angles of a quadrilateral is 360°.  
= 90° = 90°  The square symbol indicates a right angle.  
60° + + 90° + 90° = 360°  Since three of the four angle measures are given, you can find the fourth angle measurement.  
+ 240° = 360° = 120°  Calculate the measurement of, From the image, you can see that it is an obtuse angle, so its measure must be greater than 90°.  
Answer  = 120°  
The table below summarizes the special types of quadrilaterals and some of their properties.
Name of Quadrilateral  Quadrilateral  Description 
Parallelogram  2 pairs of parallel sides. Opposite sides and opposite angles are congruent.  
Rectangle 


Square 


Trapezoid  Only one pair of opposite sides is parallel. 
A quadrilateral is a mathematical name for a foursided polygon. Parallelograms, squares, rectangles, and trapezoids are all examples of quadrilaterals. These quadrilaterals earn their distinction based on their properties, including the number of pairs of parallel sides they have and their angle and side measurements. : Quadrilaterals
What triangle is more than 180 but less than 360?
An angle which measures more than 180∘ but less than 360∘, is called a an acute angle b an obtuse angle c a straight angle d a reflex angle Solve Textbooks Question Papers Install app : An angle which measures more than 180∘ but less than 360∘, is called a an acute angle b an obtuse angle c a straight angle d a reflex angle
Are all circles 360 degrees?
Full Circle In school we learn there are 360 degrees in a circle, but where did the 360 come from? When it is pointed out that the Babylonians counted to base60, rather than base10 as we do, people often ask if there is a connection. The short answer is no. The longer answer involves Babylonian astronomy.
Like other ancient peoples, the Mesopotamians observed the changing positions of the sun, moon and five visible planets (Mercury, Venus, Mars, Jupiter and Saturn) against the background of stars in the sky. Before 2000 BC a scribe in the southern city of Uruk, referring to a festival for the goddess Inanna, made it clear that, as Venus, she could be both morning and evening star, depending on whether she appeared before sunrise or after sunset.
For them, Venus was a single object and they observed its changing position, along with the other planets and the moon. These positions all lie on the same great circle, called the ecliptic, defined by the apparent motion of the sun as seen from the earth during the course of a year.
The reason the moon and planets are on the ecliptic is that, from the earth’s point of view, the plane of the solar system meets the heavenly dome in a great circle, so that is where they all appear. In order to record their motions accurately two things are needed: a fixed calendar and a method of recording positions on the ecliptic.
Calendars are tricky. The phases of the moon formed a rhythm in the life of all ancient cultures and it was natural for the Mesopotamians to base their calendar on months that started on the evening of the first crescent at sundown. With good visibility, a lunar month lasts 29 or 30 days and by about 500 BC the Babylonians had discovered a scheme for determining the start of each month.
 This used a 19year cycle: 19 years is almost exactly 235 lunar months and the scheme works on seven long years (of 13 months) and 12 short years (of 12 months).
 This led to a fixed method of interleaving long and short years, still used today in the Jewish calendar and everything in the Christian year based on the date of Easter.
The records that helped them discover this cycle began in the mideighth century BC, when Babylonian astronomers wrote nightly observations in what we now call ‘astronomical diaries’. These continue until the end of cuneiform scholarship in the first century ad, yielding eight hundred years of astronomical records: a terrific achievement, far longer than anything in Europe to this day.
It facilitated great advances, notably their discovery of the socalled Saros cycles for predicting eclipses. Each one is a cycle of 223 lunar months, perpetuated over a period of more than 1,000 years. There are Saros cycles operating today first seen in the eighth and ninth centuries. They remain the basis for eclipse prediction and appear in detail on the NASA website.
Astronomers in Babylon were using Saros cycles by the late seventh century BC. They only needed a lunar calendar to keep track of them, but for more sophisticated work on the moon and planets they needed a steady, nonlunar calendar. So they adopted an old idea, once used during the third millennium, for an administrative calendar: 12 months of 30 days in a year, making a 360day cycle.
 This ‘ideal calendar’ reappears in the second millennium BC in the Babylonian Seven Tablets of Creation, which states that the god Marduk ‘set up three stars each for the twelve months’.
 These triplets of stars corresponded to 12 divisions of the ecliptic, one for each ideal month of 30 days, but it was an idealised calendar not used in everyday life.
The 12 equal divisions for a year also applied for the day from sundown to sundown, divided into 12 beru, For example, in the Epic of Gilgamesh – written during the second millennium BC – our hero races the sun in Book IX and we are told how he progresses at each beru, eventually coming out just ahead.
 As with the ideal month, a beru was split into 30 equal sections called uš, giving 360 uš in a 24hour period.
 Each was therefore four minutes in modern terms.
 Fractions of an uš were also used: for example in the astronomical diaries we find an instance where the first appearance of the moon was visible for 3 ¾ quarters of an uš (15 minutes).
An accurate recording of time was important for these diaries and so were the positions of the moon and planets. During the fifth century BC a scheme was developed that could be broken down into fine detail: the ecliptic was divided into 12 equal sections, each split into 30 finer divisions (also called uš ), yielding 360 uš in total.
 For finer accuracy an uš was broken down into 60 divisions.
 Each of the 12 sections they labelled by a constellation of stars and, when the Greeks took on Babylonian results, they preserved these constellations, but gave them Greek names – Gemini, Cancer and Leo – most of which had the same meanings as in Babylonia.
As Greek geometry developed, it created the concept of an angle as a magnitude – for example, adding the angles of a triangle yields the same as two rightangles – but in Euclid’s Elements (c.300 BC) there is no unit of measurement apart from the rightangle.
 Then, in the second century BC, the Greek astronomer Hipparchos of Rhodes began applying geometry to Babylonian astronomy.
 He needed a method of measuring angles and naturally followed the Babylonian division of the ecliptic into 360 degrees, dividing the circle the same way.
 So, although angles come from the Greeks, the 360 degrees comes from Babylonian astronomy.
Mark Ronan is Honorary Professor of Mathematics at University College London. : Full Circle
Is a triangle 1 2 3 possible?
The answer is no. There are limits on what the lengths can be. For example, the lengths 1, 2, 3 cannot make a triangle because \begin 1 + 2 = 3\end, so they would all lie on the same line.
What are the 3 angles of a triangle?
Interior angles are three angles found inside a triangle. Exterior angles are formed when the sides of a triangle are extended to infinity. Therefore, exterior angles are formed outside a triangle between one side of a triangle and the extended side. Each exterior angle is adjacent to an interior angle.
Is a right triangle 180?
Right triangles are triangles in which one of the interior angles is 90 degrees, a right angle. Since the three interior angles of a triangle add up to 180 degrees, in a right triangle, since one angle is always 90 degrees, the other two must always add up to 90 degrees (they are complementary). Either of the legs can be considered a base and the other leg would be considered the height (or altitude), because the right angle automatically makes them perpendicular. If the lengths of both the legs are known, then by setting one of these sides as the base b and the other as the height h, the area of the right triangle is easy to calculate using the standard formula for a triangle’s area: This is intuitively logical because another congruent right triangle can be placed against it so that the hypotenuses are the same line segment, forming a rectangle with sides having length b and width h, The area of the rectangle is ( b )( h ), so either one of the congruent right triangles forming it has an area equal to half of that rectangle.
Is 180 a perfect triangle?
Every triangle’s three angles should always equal 180 degrees.
Do all 4 sided shapes have 360 degrees?
Quadrilaterals
 Quadrilaterals
 Learning Objective(s)
 · Identify properties, including angle measurements, of quadrilaterals.
are a special type of polygon. As with triangles and other polygons, quadrilaterals have special properties and can be classified by characteristics of their angles and sides. Understanding the properties of different quadrilaterals can help you in solving problems that involve this type of polygon.
Picking apart the name “quadrilateral” helps you understand what it refers to. The prefix “quad” means “four,” and “lateral” is derived from the Latin word for “side.” So a quadrilateral is a foursided polygon. Since it is a, you know that it is a twodimensional figure made up of straight sides. A quadrilateral also has four angles formed by its four sides.
Below are some examples of quadrilaterals. Notice that each figure has four straight sides and four angles. Interior Angles of a Quadrilateral The sum of the interior angles of any quadrilateral is 360°. Consider the two examples below. You could draw many quadrilaterals such as these and carefully measure the four angles. You would find that for every quadrilateral, the sum of the interior angles will always be 360°. You can also use your knowledge of triangles as a way to understand why the sum of the interior angles of any quadrilateral is 360°. These measurements add up to 180º. Now look at the measurements for the other triangles—they also add up to 180º! Since the sum of the interior angles of any triangle is 180° and there are two triangles in a quadrilateral, the sum of the angles for each quadrilateral is 360°. Specific Types of Quadrilaterals Let’s start by examining the group of quadrilaterals that have two pairs of parallel sides. These quadrilaterals are called They take a variety of shapes, but one classic example is shown below. Imagine extending the pairs of opposite sides. They would never intersect because they are parallel. Notice, also, that the opposite angles of a parallelogram are congruent, as are the opposite sides. (Remember that “congruent” means “the same size.”) The geometric symbol for congruent is, so you can write and,
The parallel sides are also the same length: and, These relationships are true for all parallelograms. There are two special cases of parallelograms that will be familiar to you from your earliest experiences with geometric shapes. The first special case is called a, By definition, a rectangle is a parallelogram because its pairs of opposite sides are parallel.
A rectangle also has the special characteristic that all of its angles are right angles; all four of its angles are congruent. The other special case of a parallelogram is a special type of rectangle, a, A square is one of the most basic geometric shapes. It is a special case of a parallelogram that has four congruent sides and four right angles. A square is also a rectangle because it has two sets of parallel sides and four right angles. A square is also a parallelogram because its opposite sides are parallel. So, a square can be classified in any of these three ways, with “parallelogram” being the least specific description and “square,” the most descriptive. In summary, all squares are rectangles, but not all rectangles are squares. All rectangles are parallelograms, but not all parallelograms are rectangles. And all of these shapes are quadrilaterals. The diagram below illustrates the relationship between the different types of quadrilaterals. You can use the properties of parallelograms to solve problems. Consider the example that follows.
Example  
Problem  Determine the measures of and,  
is opposite is opposite  Identify opposite angles.  
A property of parallelograms is that opposite angles are congruent.  
= 60°, so = 60° = 120°, so = 120°  Use the given angle measurements to determine measures of opposite angles.  
Answer  = 60° and = 120° 
There is another special type of quadrilateral. This quadrilateral has the property of having only one pair of opposite sides that are parallel. Here is one example of a, Notice that, and that and are not parallel. You can easily imagine that if you extended sides and, they would intersect above the figure.
If the nonparallel sides of a trapezoid are congruent, the trapezoid is called an, Like the similarly named triangle that has two sides of equal length, the isosceles trapezoid has a pair of opposite sides of equal length. The other pair of opposite sides is parallel. Below is an example of an isosceles trapezoid.
In this trapezoid ABCD, and,
A) Some trapezoids are parallelograms. Incorrect. Trapezoids have only one pair of parallel sides; parallelograms have two pairs of parallel sides. A trapezoid can never be a parallelogram. The correct answer is that all trapezoids are quadrilaterals. B) All trapezoids are quadrilaterals. Correct. Trapezoids are foursided polygons, so they are all quadrilaterals. C) All rectangles are squares. Incorrect. Some rectangles may be squares, but not all rectangles have four congruent sides. All squares are rectangles however. The correct answer is that all trapezoids are quadrilaterals. D) A shape cannot be a parallelogram and a quadrilateral. Incorrect. All parallelograms are quadrilaterals, so if it is a parallelogram, it is also a quadrilateral. The correct answer is that all trapezoids are quadrilaterals. 
You can use the properties of quadrilaterals to solve problems involving trapezoids. Consider the example below.
Example  
Problem  Find the measure of,  
= 360°  The sum of the measures of the interior angles of a quadrilateral is 360°.  
= 90° = 90°  The square symbol indicates a right angle.  
60° + + 90° + 90° = 360°  Since three of the four angle measures are given, you can find the fourth angle measurement.  
+ 240° = 360° = 120°  Calculate the measurement of, From the image, you can see that it is an obtuse angle, so its measure must be greater than 90°.  
Answer  = 120°  
The table below summarizes the special types of quadrilaterals and some of their properties.
Name of Quadrilateral  Quadrilateral  Description 
Parallelogram  2 pairs of parallel sides. Opposite sides and opposite angles are congruent.  
Rectangle 


Square 


Trapezoid  Only one pair of opposite sides is parallel. 
A quadrilateral is a mathematical name for a foursided polygon. Parallelograms, squares, rectangles, and trapezoids are all examples of quadrilaterals. These quadrilaterals earn their distinction based on their properties, including the number of pairs of parallel sides they have and their angle and side measurements. : Quadrilaterals