Question

In the given figure, if AB is the diameter of the circle and PM the internal bisector of $\angle APB$, then the measure of angle ABM is

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${45}^{\circ }$

$\angle APB={90}^{\circ }$ (Angle in a semcircle is a right angle)
$\Rightarrow \angle APM=\frac{1}{2}\angle APB={45}^{\circ }$ (PM bisects $\angle APB$)
$\therefore \angle ABM=\angle APM={45}^{\circ }$(Angles in the same segment are equal