Question

what is the measure of ∠abc?

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Identify the intercepted arc

The inscribed angle $\angle ABC$ intercepts arc $AC$, and the measure of arc $AC$ is $130^{\circ}$.

Step3: Calculate the measure of the inscribed angle

Let $m\angle ABC$ be the measure of the inscribed angle. By the inscribed - angle theorem, $m\angle ABC=\frac{1}{2}\times$ measure of arc $AC$. So $m\angle ABC = \frac{1}{2}\times130^{\circ}=65^{\circ}$.

Answer:

D. $65^{\circ}$