Answer
$\bf{C}$
Work Step by Step
Since the measure of an inscribed angle is equal to half the measure of its intercepted arc:
Thus, $\angle c=\dfrac{50^{\circ}}{2}=25^{\circ}$
Given: $\angle a=90^{\circ}$
The sum of all interior angles in a triangle is $180^{\circ}$, so we can find $\angle b$ as:
$\angle b +90^{\circ}+25^{\circ}=180^{\circ}\\ \angle b =180^{\circ} -115^{\circ}\\ \angle b=65^{\circ}$
Therefore, the correct option is $\bf{C}$.
