Why Does a Triangle Have 180 Degrees?

You know how the angles of a triangle always add up to 180⁰? Why is that? After all, 180⁰ is the angle that stretches from one side of a straight line to another—so it’s kind of weird that that’s the number of degrees in the angles of a triangle.

What in the world does a triangle have to do with a single straight line? As it turns out, quite a lot. And triangles also have a lot to do with rectangles, pentagons, hexagons, and the whole family of multi-sided shapes known as polygons.

We’ll see exactly what I mean by this over the next few weeks. But for today, we’re going to start by figuring out exactly why it is that the angles of a triangle always add up to 180⁰. Or so you thought … because we're also going to see that sometimes they don't.

First, a review: types of triangles

A quick refresher: there are three different types of basic triangles. They are equilateral, isosceles, and scalene.

• An equilateral triangle has three sides of the same length
• An isosceles triangle has two sides of the same length and one side of a different length
• A scalene triangle has three sides of all different lengths

The length of a triangle's side directly affects its angles.

RELATED: What is Pascal's Triangle?

Interior and exterior angles

Before we get too far into our story about triangles and the total number of degrees in their three angles, there's one little bit of geometric vocabulary that we should talk about. And that is the difference between an interior and an exterior angle.

The easiest way to describe the difference between these two things is with an example. Since today's theme is the triangle, let's talk about the interior and exterior angles of a triangle. In short, the interior angles are all the angles within the bounds of the triangle. In other words, they're the kind of angles we've been talking about all along.

The exterior angles of a triangle are all the angles between one side of the triangle and the line you get by extending a neighboring side outside the bounds of the triangle. If you think about it, you'll see that when you add any of the interior angles of a triangle to its neighboring...

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