In geometry, what's the sum of the three angles of a triangle?

And the answer: 180.    

In basic geometry, the three interior angles of any triangle always add up to 180. So if you know two of the angles, you can easily figure out the third by subtracting each angle from 180.

Photo credit: Nina Aldin Thune via Wikimedia Commons

Triangles are special polygons that always have three sides and three angles. They can be classified by their angles or by their sides. For starters, there can be right triangles, acute triangles, or obtuse triangles. While all triangles always have at least two acute angles (measuring less than 90°), the third can be the defining factor in its classification. Take a look below.

From left to right: acute, right, obtuse. Photo credit:
A quick refresher from math class: Triangles with a 90° angle (known as a right angle) are right triangles, and those with an angle greater than 90° are obtuse.

Triangles can also be classified by their sides. By measuring the sides of the triangle, we can place it in one of three additional categories: equilateral, isosceles, and scalene. Equilateral triangles are exactly how they sound: three sides of equal length (and, naturally, three angles equal in measure). Isosceles triangles have only two equal sides, while scalene triangles have three sides of all different measures.

By combining these measures of size and angle, we can further identify types of triangles. For example, an acute scalene triangle is a perfectly practical figure, as is an isosceles right triangle. However, there are some combinations of size and angle that are impossible. Because right triangles must have at least one angle measure of 90°, and equilateral triangles must have three equal sides, no equilateral triangle can also be a right triangle. Additionally, equilateral triangles can not be obtuse because, again, they must have three equal sides (doesn't leave much room for obtuse angles, does it?).

Learn more about the qualities of triangles here.

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