Study guides › Level 7 · Geometry

Angles in a triangle

Level 7 · Geometry · for questions like “A triangle has angles of 50° and 60°. What is the third angle?”

💡 The idea

The three angles inside any triangle always add up to 180°.

🪜 The steps

1. Missing angle: 180° minus the two you know.
2. Isosceles triangle (two equal sides): the two base angles are equal. Take the top angle from 180°, then halve what's left.
3. Outside angle (one side extended): it equals the two inside angles that aren't next to it, added together.

✏️ Worked examples

1. 50° and 60°: 180 − 50 − 60 = 70°.

2. Isosceles with a 40° top angle: 180 − 40 = 140, and ÷ 2 = 70° each.

3. Inside angles of 45° and 65°, outside angle at the third corner: 45 + 65 = 110°.

⚠️ Watch out

• Don't stop at the inside angle when the question asks for the outside one. The two make a straight line, 180°.

🎯 Try these

1. Angles of 35° and 85°. Third angle?
2. Isosceles with a 100° top angle. Each base angle?
3. Inside angles of 30° and 70°. The outside angle at the third corner?

Answers: 1) 60° 2) 40° 3) 100°

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.