Question

In the above figure, O is the centre of the circle. The angle CBD is equal to

• A. ${25}^{\circ }$
• B. ${50}^{\circ }$
• C. ${40}^{\circ }$
• D. ${130}^{\circ }$

Answer 1

The correct option is A ${25}^{\circ }$

$\because$ Angle subtended by Arc ABC at the centre
$O={50}^{\circ }$
$\therefore$ Angle subtended by Arc ABC at any point on the circumference $={25}^{\circ }$
$\therefore \angle ABC={180}^{\circ }-{25}^{\circ }={155}^{\circ }$
[Since opposite angles of a cyclic quadrilateral are supplementary]
$\therefore \angle CBD={180}^{\circ }-{155}^{\circ }={25}^{\circ }$