Question

Find the value of $x$ in the following figure.

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

Consider $\Delta ABO$,
AO=BO ( radii of the same circle)
$\angle OAB=\angle OBA={30}^{\circ }$
$\to \angle AOB={120}^{\circ }$.

$\angle ACB=\frac{1}{2}\times \angle AOB={60}^{\circ }$ (angle subtended by chord on major arc is half of the angle subtended on the center.)

Thus $\angle ADB=\angle ACB$ (equal angles)
$\to x={60}^{\circ }$