Interior angles of a triangle
Key idea / 要点
The three interior angles of any triangle add up to 180°.
So if you know two angles, subtract from 180° to find the third. For example, a triangle with 50° and 60° has a third angle of 180° − 50° − 60° = 70°.
Exterior angle of a triangle
If one side of a triangle is extended, the angle formed outside is an exterior angle. It sits on a straight line with its neighbouring interior angle, so together they make 180°.
Key idea / 要点
An exterior angle of a triangle equals the sum of the two opposite (non-adjacent) interior angles.
Worked example / 例题
A triangle has interior angles 45° and 65°. One side is extended. Find the exterior angle at the third vertex.
Third interior angle = 180° − 45° − 65° = 70°.
Exterior angle = 180° − 70° = 110°.
Check with the exterior-angle rule: 45° + 65° = 110°. Same answer. Correct.
Remember / 记住
- Interior angles of a triangle add to 180°.
- Exterior angle = sum of the two opposite interior angles.
- Exterior angle + its adjacent interior angle = 180°.