Question

In a circle with centre O. seq PQ , is a chord such that $\angle POQ={70}^o$. Find the $\angle OPQ$

Answer 1

REF.image

Given,$\angle PCQ={70}^{\circ }$

here $OP=OQ$ [ seine both are radius of the circle with angles ]

$\therefore \Delta OPQ$ is an is isocles

$\therefore \angle OPQ=OQP$ ...(1)

In $\Delta OPQ,$

using angle sum properly

$\angle OPQ+\angle POQ+\angle OQP={180}^{\circ }$

$\angle OPQ+{70}^{\circ }+\angle OPQ={180}^{\circ }\left[fromQ\right]$

$\angle OPQ={180}^{\circ }-{70}^{\circ }$

$\Rightarrow \angle OPQ=\frac{{110}^{\circ }}{2}$

$\therefore \angle OPQ={55}^{\circ }$