Question

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

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc.

Step2: Calculate the inscribed - angle measure

Let the central angle be $\theta_{c}=90^{\circ}$, and the inscribed angle be $\theta_{i}$. According to the formula $\theta_{i}=\frac{1}{2}\theta_{c}$. Substituting $\theta_{c} = 90^{\circ}$ into the formula, we get $\theta_{i}=\frac{1}{2}\times90^{\circ}=45^{\circ}$.

Answer:

A. $45^{\circ}$