Question

Given a circle with O as the centre. Find the value of x.

• A. ${30}^{\circ }$
• B. ${40}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${40}^{\circ }$

$\Delta AOB$ is an isosceles triangle. $(\because in\Delta AOB;OA=OB;Radii)$

$\Rightarrow \angle OAB=\angle OBA={50}^{\circ }$

$\text{In}\Delta AOB,$

$\angle OAB+\angle OBA+\angle AOB={180}^{\circ }$

$\text{Hence,}\angle AOB={80}^{\circ }$

The angle subtended by an arc of the circle at its centre is double the angle subtended by it at any point on the remaining part of the circle.
Therefore,
$\angle ACB=\frac{1}{2}\angle AOB={40}^{\circ }$