Question : In the given figure, O is the centre of the circle, $\angle PQO=30^{\circ}$ and $\angle QRO=45^{\circ}$. What is the value (in degrees) of $\angle POR$?
Option 1: $150^{\circ}$
Option 2: $110^{\circ}$
Option 3: $160^{\circ}$
Option 4: $130^{\circ}$
Correct Answer: $150^{\circ}$
Solution :
Given: $\angle PQO=30^{\circ}$ and $\angle QRO=45^{\circ}$
Since $OQ$ and $OR$ is the radius,
So, $\angle OQR=45^{\circ}$
$⇒\angle POR=2(\angle PQO+\angle OQR)$ (By angle subtended by minor arc.)
$\therefore \angle POR=2(30^{\circ}+45^{\circ})=2×75^{\circ}=150^\circ$
Hence, the correct answer is $150^\circ$.
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