### 4) Angles in a semicircle

The angle at the circumference in a **semicircle** is a right angle.

Angle APB = 90°

#### Example

Calculate the angle *z*.

The angle at the circumference in a semi-circle is 90°.

Angle STU = 90°

Angles in a triangle add up to 180°.

*z *= 180° – 90° – 31° = 59°

#### Proof

The angle on a straight line is 180°. The angle VOY = 180°.

The angle at the centre is double the angle at the circumference.

Angle VWY = 1/2 of angle VOY = 1/2 x 180°.

Angle VWY = 90°