Question

In the given figure, $O$ is the centre of the circle. Find $x$.

• A. 50°
• B. 40°
• C. 30°
• D. 20°

Answer 1

The correct option is B

40°

The angle subtended by an arc at the centre is double than the angle subtended by it at any point on the remaining part of the circle.

$\Rightarrow \angle AOC=2\angle ABC[\angle ABC={50}^{\circ }]$

$\Rightarrow \angle AOC=2\times {50}^{\circ }={100}^{\circ }$

$\angle OAC=\angle OCA\text{[OA = OC (radii of circle)]}$

$\text{In}△AOC,$

$x+x+\angle AOC={180}^{\circ }$ [Angle sum property]

$\Rightarrow 2x={180}^{\circ }-{100}^{\circ }$

$\Rightarrow x={40}^{\circ }$