Revision notes
Discover why the angles of every triangle add up to 180° and use it to find missing angles.
Look at a roof frame or the steel of a bridge — triangles everywhere! Triangles are strong because their shape can't be squashed. And every triangle, big or small, hides the same secret about its angles. Let's find it.
A triangle has 3 sides, 3 corners (vertices) and 3 angles inside.
We name the angles by their corners: angle A, angle B, angle C.
Angles are measured in degrees (°). A right angle — like the corner of your exercise book — is 90°. A straight line is 180°.
No matter how you drag it, the three angles always add up to 180°.
If you tore off the three corners of a paper triangle and put them side by side, they would make a straight line — and a straight line is 180°.
So if you know two angles, you can always find the third.
🔑 Key idea: Angles in a triangle add up to 180°.
A = 50°, B = 60°. Find C.
Step 1: Use the angle sum of a triangle
A + B + C = 180°
Step 2: Add the angles you know
50° + 60° = 110°
Step 3: Subtract from 180°
C = 180° − 110° = 70°
Why? Whatever is left over from 180° must be the missing angle.
Answer: C = 70°
Right-angled: one angle is 90°, so the other two add up to 90°.
Isosceles: two sides are equal, and the two angles opposite them (the base angles) are equal.
Equilateral: all sides equal, all angles equal — 180° ÷ 3 = 60° each.
🔑 Key idea: Equal sides ↔ equal angles.
Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.