Question

In the figure given below, if $\angle AOP={75}^{\circ }$ and $\angle AOB={120}^{\circ }$, the what is $\angle AQP$?

• A. ${45}^{\circ }$
• B. ${37.5}^{\circ }$
• C. ${30}^{\circ }$
• D. ${22.5}^{\circ }$

Answer 1

The correct option is B ${37.5}^{\circ }$

Here, $\angle AOP$ is subtended by the arc AP at the centre of the circle. And, $\angle AQP$ is subtended by the arc AP at the point Q on the circle.
We know that the angle subtended by an arc of a circle at the centre of the circle is double the angle subtended by it at any point on the circle.
So, $\angle AOP=2\angle AQP$
$\Rightarrow \angle AQP=\frac{1}{2}\angle AOP=\frac{1}{2}\times {75}^{\circ }={37.5}^{\circ }$