Angles in a semicircle - Higher
The angle at the Circumference is the name of the perimeter of a complete circle, that is, the distance all around it. in a A diameter divides a circle into two semicircles. is a right angle.
Angle APB = 90°
Example
Calculate the angle \(z\).
The angle at the circumference in a semicircle is 90°.
Angle STU = 90°
Angles in a triangle add up to 180°.
\(z = 180 - 90 - 31 = 59^\circ\)
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 = \(\frac{1}{2}\) of angle VOY = \(\frac{1}{2} \times 180\).
Angle VWY = 90°