Plz see the attachement and answer the question?

Feb 8, 2018

$\angle Q S R = {78}^{\circ}$

Explanation:

As $Q R$ subtends the angles $\angle Q P R$ and $\angle Q S R$ on thesame side of chord $Q R$, thetwo are equal i.e.

$\angle Q S R = \angle Q P R$

As $Q S$ is bisector of $\angle P Q R$ and $\angle S Q R = {35}^{\circ}$

$\angle P Q R = 2 \times {35}^{\circ} = {70}^{\circ}$

Now in $\Delta P Q R$, we have $\angle P Q R = {70}^{\circ}$ and $\angle P R Q = {32}^{\circ}$

Hence $\angle Q P R = {180}^{\circ} - {70}^{\circ} - {32}^{\circ} = {78}^{\circ}$

and $\angle Q S R$ too is ${78}^{\circ}$.