Question

In the given figure, O is the centre of the circle, the value of x is

• A. ${65}^{\circ }$
• B. ${55}^{\circ }$
• C. ${75}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is B

${55}^{\circ }$

We have $\angle QPS={90}^{\circ }$ [Angles in a semicircle]
In $\Delta PQS$
$\angle PSQ+\angle SQP+\angle QPS={180}^{\circ }$ [Sum of angles of a triangle is ${180}^{\circ }$]
$\Rightarrow \angle PSQ={180}^{\circ }-{90}^{\circ }-{35}^{\circ }={55}^{\circ }$
Then, x = $\angle PSQ$ [Angles in the same segment]
$={55}^{\circ }$