Question

In the given figure, if $\angle AOD=$ ${135}^{\circ }$ then $\angle BOC$ is equal to

(a) ${25}^{\circ }$ (b) ${45}^{\circ }$ (c) ${52.5}^{\circ }$ (d) ${62.5}^{\circ }$

Answer 1

The correct option is (b): ${45}^{\circ }$

We know that the sum of angles subtended by opposite sides of a quadrilateral having a circumscribed circle is 180 degrees
$\angle AOD+\angle BOC={180}^{\circ }$
$\angle BOC={180}^{\circ }-{135}^{\circ }={45}^{\circ }$