Question

question 1 of 10 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 intercepted arc of \(\angle ABC\) is the arc \(AC\) which has a measure of \(130^{\circ}\).

Step3: Calculate the measure of \(\angle ABC\)

Let \(m\angle ABC\) be the measure of the inscribed - angle and \(m\overset{\frown}{AC}\) be the measure of the intercepted arc. Then \(m\angle ABC=\frac{1}{2}m\overset{\frown}{AC}\). Substituting \(m\overset{\frown}{AC} = 130^{\circ}\), we get \(m\angle ABC=\frac{130^{\circ}}{2}=65^{\circ}\).

Answer:

C. \(65^{\circ}\)