Measuring the Angles of Triangles: 180 Degrees

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  • 0:05 A Triangle
  • 0:24 Three Angles
  • 0:50 The Formula and Proof
  • 2:22 Finding a Missing Angle
  • 4:00 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to see why a triangle's angles always add up to 180 degrees. Also, learn how you can use this unique fact about triangles to find an unknown angle in a triangle.

A Triangle

If you cut a rectangular piece of cake in half diagonally, you will end up with two triangles. In this video lesson, we will talk about the angles of a triangle and why they always add up to 180 degrees. We can define a triangle as a flat shape with three straight sides.

Three Angles

The angles of the triangle are the inside corners of a triangle. You can see that there are three of them. No matter what size or kind of triangle you have, you will always have your three angles. Do you see the three angles in all of these triangles? We can label our three angles as a, b, and c. It doesn't matter which one we label which as long as all three are labeled.

Three sides to a triangle
Girl and triangle

The Formula and Proof

With our angles labeled, we have a formula we can refer to for the angles. It is a + b + c = 180, which tells us that if we add up all of our angles, they will always equal 180.

Why is this? Well, we can prove this with the use of parallel lines. If we extended the line between angles a and b and we drew a line through the tip of angle c that is parallel to the line going through the point of angles a and b, then we will see that all three angles add up to 180 degrees.

If you look at the parallel lines we've drawn and you compare the angles, you will see that angles a and b are the same angles as the angles on either side of angle c. Each side of the triangle becomes the line that intersects the pair of parallel lines, and because of this, the angles that are inside the parallel lines and on opposite sides of the intersecting line are equal.

Another way you can check this is to draw a triangle using a ruler. Then cut it out and then tear each angle off. Then connect the angles. What do they form? Don't they form a straight line at the bottom? This is the same kind of proof as the parallel lines proof. It shows you that all three angles always add up to 180 degrees, or a straight line.

Finding a Missing Angle

Because all triangles add up to 180 degrees, we can use this fact to our advantage. Sometimes we will have a triangle for which we know the measurement of two of the angles. The unknown third angle is easy to find since we know that all of them added up will equal 180. To find the missing angle, we can either use the formula and a bit of algebra or simply subtract the two known angles from 180 to find the unknown third.

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