Question

part b
what is the measure of the central angle if the corresponding inscribed angle measures 45°?
show hints
45°
135°
90°
105°

Explanation:

Step1: Recall the inscribed - central angle relationship

The measure of a central angle is twice the measure of an inscribed angle subtended by the same arc.

Step2: Calculate the central - angle measure

Let the inscribed angle $\theta_{i}=45^{\circ}$. Then the central angle $\theta_{c}=2\times\theta_{i}$. So $\theta_{c}=2\times45^{\circ}=90^{\circ}$.

Answer:

C. $90^{\circ}$