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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: $130^{\circ}$


Team Careers360 23rd Jan, 2024
Answer (1)
Team Careers360 24th Jan, 2024

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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