Finding the third angle of a triangle when you know the other two?
I'm stuck on a geometry problem. It says two angles in a triangle are 50° and 70°. I need to find the measure of the third angle, but I also have to explain *how* I know the answer.
I feel like there's a simple rule for this but I can't remember what it is. Can someone explain the steps and the reason behind it? Thanks!
3 Answers
Hi @Lucas_Jensen, you're right, there's a straightforward rule for this!
The Rule: The sum of the interior angles in any triangle always equals 180 degrees. This is a fundamental property of triangles, often called the Triangle Angle-Sum Theorem.
Here's how to solve it step-by-step:
- Add the known angles: 50° + 70° = 120°
- Subtract the sum from 180: 180° - 120° = 60°
So, the measurement of the third angle is 60 degrees.
The "how do you know" part is the rule itself: you know because the angles in a triangle must always add up to 180°.
The third angle is 60 degrees.
You know because a triangle's angles always add up to 180. Just do 180 - 50 - 70.
The answer is 60°.
As to the 'why', a cool way to visualize it is to imagine drawing a line through one of the triangle's vertices (corners) that is parallel to the opposite side. Because of the rules for parallel lines and transversals, you'll see that the three angles of the triangle perfectly line up to form a straight line. A straight line is 180 degrees. That's a quick visual proof for why the rule works!