Question

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

Answer 1

Given:

$\angle PQR={100}^{\circ }$

$\angle POR=2\times \angle PQR=2\times 100°=200°$

$\therefore \angle POR=360°-200°=160°$

In $\Delta OPR$,

$\Rightarrow$$OP=OR$ ...Radii of the circle

$\Rightarrow$$\angle OPR=\angle ORP$

Now,
$\angle OPR+\angle ORP+\angle POR=180°$ ...Sum of the angles in a triangle

$\Rightarrow \angle OPR+\angle OPR+160°=180°$

$\Rightarrow 2\angle OPR=180°-160°$

$\Rightarrow \angle OPR=10°$