Question

In the given figure, O is the centre of the circle $\angle PBA={45}^{\circ }$. The value of $\angle PQB$ is

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

Answer 1

The correct option is B

${45}^{\circ }$

We have $\angle APB={90}^{\circ }$ [Angle in a semicircle]
In $\Delta APB,\angle A+\angle B+\angle P={180}^{\circ }$ [Sum of angles of a triangle is ${180}^{\circ }$]
$\Rightarrow y^{\circ }+{45}^{\circ }+{90}^{\circ }={180}^{\circ }$
$\Rightarrow y^{\circ }={180}^{\circ }-{45}^{\circ }-{90}^{\circ }$
$\Rightarrow y^{\circ }={45}^{\circ }$
Now, $\angle PAB=\angle PQB$ [Angles in the same segment]
Hence, $\angle PQB={45}^{\circ }$