Angles in triangles

The three angles inside any triangle always add up to 180°. So if you know two of them, you can always find the third.

Key facts

  • Angles in a triangle add up to 180°.
  • In an isosceles triangle, the two base angles are equal.
  • In an equilateral triangle, every angle is 60°.
  • An exterior angle equals the two opposite interior angles added together.

Worked examples

Example 1

Find the angle x.

  1. The angles in a triangle add up to 180°. x + 50 + 70 = 180
  2. Take both known angles away from 180. x = 180 − 50 − 70
  3. Work it out. x = 60°

Answer: x = 60°

Example 2

This triangle is isosceles. The top angle is 40°. Find each base angle y.

  1. Take the top angle from 180. 180 − 40 = 140
  2. The two base angles are equal, so share it equally. 140 ÷ 2 = 70
  3. So each base angle is: y = 70°

Answer: y = 70°

Questions about angles in triangles