How numerous degrees perform the three angles the a triangle contain? They've acquired 180 that 'em, right? Why 180 and not some other number? and also do every triangles yes, really contain 180 degrees? save on analysis to find out!


*

us are currently experiencing playback worries on Safari. If friend would prefer to listen to the audio, please use Google Chrome or Firefox.
The Quick and Dirty A triangle's angles include up to 180 degrees since one exterior edge is same to the sum of the other two angles in the triangle. In various other words, the other two angles in the triangle (the persons that add up to form the exterior angle) must combine with the 3rd angle to make a 180 angle.

You are watching: Why is it impossible for a triangle to contain a 180° angle?


You know how the angle of a triangle always add up to 1800? Why is that? after ~ all, 1800is the angle that stretches indigenous one next of a straight line to another—so it’s type of weird that that’s the number of degrees in the angle of a triangle.What in the world does a triangle need to do with a solitary straight line? as it transforms out, quite a lot. And triangles also have a many to execute with rectangles, pentagons, hexagons, and also the totality family of multi-sided shapes recognized as polygons.We’ll see specifically what I median by this over the next couple of weeks. Yet for today, we’re walk to begin by figuring out exactly why the is that the angles of a triangle always add up come 1800. Or so you assumed … because we're likewise going to watch that occasionally they don't.

*

*
*

*
*

*
*

Types of triangles

A fast refresher: there room three different species of straightforward triangles. They room equilateral, isosceles, and scalene.An it is intended triangle has three political parties of the same lengthAn isosceles triangle has two sides of the exact same length and also one next of a different lengthA scalene triangle has actually three sides of all different lengthsThe length of a triangle's side straight affects the angles.RELATED: What is Pascal's Triangle?

Interior and also exterior angles

Before we get too much into ours story around triangles and the total variety of degrees in their 3 angles, there's one small bit the geometric vocabulary the we should talk about. And also that is the difference in between an interior and an exterior angle.The easiest way to describethedifference in between these two things is with an example. Since today's layout is the triangle,let'stalk about the interior and also exterior angles of a triangle. In short, theinterior anglesare all the angleswithinthe border of the triangle. In various other words, they're the sort of angle we've to be talking around all along.
*
Theexterior anglesof a triangleare every the angles in between one next of the triangle andthe heat you gain by extending a surrounding sideoutsidethe limit of the triangle. If girlfriend think around it, you'll check out that when you include any that theinterior angles of a triangletoitsneighboringexterior angle,you always get1800—a directly line.

How numerous degrees is a triangle?

Which brings us to the key question because that today: Why is it that the interior angles the a triangle always add up come 1800? as it turns out, you can figure this the end by thinking around the interior and also exterior angle of a triangle. To check out what ns mean, one of two people grab your creativity or a paper of file because it’s time because that a little mathematical arts-and-crafts illustration project.Start by drawing a best triangle with one horizontal leg, one upright leg, and also with the hypotenuse prolonging from the height left come the bottom right. Now make a copy the this triangle, rotate it roughly 1800, and also nestle it increase hypotenuse-to-hypotenuse with the initial (just together we did as soon as figuring out exactly how to discover the area that a triangle). Finally, do yet an additional copy of the original triangle and transition it to the ideal so the it’s sit right alongside the newly-formed rectangle. V me therefore far? If so, your snapshot should look like this:
*
What’s the point of this picture? take a look in ~ the internal angle in ~ the bottom ideal of the initial triangle (the one labeling “A”). Currently take a look at the two angles that comprise the exterior angle because that that edge of the triangle (the ones labeling “B” and “C”). As we know, if we include up the interior and also exterior angles of one corner of a triangle, we constantly get 1800. And also our small drawing reflects that the exterior edge in inquiry is equal to the sum of the other two angle in the triangle. In other words, the other two angle in the triangle (the people that add up to kind the exterior angle) must combine with the angle in the bottom right edge to make a 1800 angle.RELATED: The people of TrigonometryFor the sake of simplicity, we’ve made our drawing using a best triangle. Yet it turns out that you have the right to make an specifically analogous illustration using any kind of triangle friend fancy, and also you’ll constantly end up reaching the same conclusion. Shot making a few drawings beginning with various triangles the your choosing to view this because that yourself. Together an example, here’s an additional one that I’ve made:
*
The unpreventable conclusion that this video game is the the interior angles that a triangle need to always include up to 1800. Our lovely and elegant tiny drawing proves the this should be so.Or go it?

Do all triangles same 180 degrees? have the right to triangles have actually more?

Might there be some limitation come our drawing that is blinding united state to part other much more exotic possibility? Here’s something for you to think around or try. Procure an uninflated balloon, lay that on a flat surface, and also draw together close to as perfect the a triangle on it together you can. If you have actually a protractor handy, it’d be an excellent to measure and add up the triangle’s interior angles and check the they’re nice close come 1800.Now blow up the balloon and also take a watch at your triangle. What occurred to it? If you have that protractor, shot once again to sum up its inner angles. What happened to this sum? execute you still gain 1800? What does this all mean when it concerns the concern of even if it is or not the interior angles the a triangle always add up to 1800as we seem to have actually found?Thankfully, I have the answer. Head on over to next week's article where us started trying out the strange and wonderful people known as non-Euclidean geometry.

See more: Can You Pass Out From Locking Your Knees, Causes Of Fainting: Reasons Why We Pass Out


Jason Marshall is the writer of The mathematics Dude's Quick and also Dirty overview to Algebra. He gives clear explanations of math terms and also principles, and his simple tricks for solving simple algebra troubles will have also the many math-phobic human being looking front to functioning out whatever math problem comes your way.