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 of the angle subtended by it at any point on the remaining part of the circle.

$\angle AOC=2\angle ABC$ [$\angle ABC={50}^{\circ }$]
$\Rightarrow \angle AOC=2\times {50}^{\circ }={100}^{\circ }$
$\angle OAC=\angle OCA$ [OA = OC (Radii of circle)]

In $△AOC,$

$\angle OAC+\angle OCA+\angle AOC={180}^{\circ }$]
$x+x+\angle AOC={180}^{\circ }$ [Sum of angles of a triangle is ${180}^{\circ }$]
$2x={180}^{\circ }-{100}^{\circ }$
$x={40}^{\circ }$