Question

In the given figure, $\angle$PQR$={100}^o$, where P, Q and R are points on a circle with centre O. Then $\angle$OPR is ___________.

• A. ${20}^o$
• B. ${10}^o$
• C. ${30}^o$
• D. ${40}^o$

Answer 1

The correct option is B ${10}^o$

$\angle PQR$ is half of the reflex $\angle POR$, then

$\angle POR=360-200={160}^o$

$\angle OPR=\angle ORP$ (because OP and OR are radius of circle)

$\therefore \angle OPR=\frac{1}{2}(180-\angle POR)={10}^o$