Angles in triangles · Grade 8

In Grade 8 you learn: exterior angles of triangles and proofs with triangles.

The three angles inside any triangle always add up to 180°. Combined with facts about isosceles and equilateral triangles, this lets you find any missing angle, and the exterior-angle rule gives a useful shortcut.

Key facts

  • Angles in a triangle add up to 180°.
  • In an isosceles triangle the two base angles (opposite the equal sides) are equal.
  • In an equilateral triangle every angle is 60°.
  • In a right-angled triangle the other two angles add up to 90°.
  • An exterior angle equals the sum of the two opposite interior angles.

Worked examples

Example 1

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

Answer: y = 70°

Example 2

In triangle ABC, angle A = x, angle B = 2x and the exterior angle at C is 135°. Find x.

Answer: x = 45°

Other years