Question

Match the unknown angle $x$ in each case if O is the centre of each circle.

• A. ${40}^{\circ }$
• B. ${30}^{\circ }$
• C. ${90}^{\circ }$

Answer 1

Since the angle subtended by an arc at the centre of a circle is double the angle subtended by it on any remaining part of the circle,
$x=\angle AEB=\frac{1}{2}\angle AOB$$=\frac{1}{2}\times {80}^{\circ }={40}^{\circ }$


$x=\angle ACB=\frac{1}{2}\angle AOB$$=\frac{1}{2}\times {60}^{\circ }={30}^{\circ }$



it can be noted that $\angle ACB$ is an angle subtended by the diameter of the circle.
Since the angle in a semicircle is a right angle, we have
$x=\angle ACB={90}^{\circ }$