Question

question 8 of 10 what is the measure of ∠abc? 130° 40° a. 40° b. 130° c. 170° d. 85°

Explanation:

Step1: Recall the 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 \(AE\). The measure of arc \(AE\) is \(170^{\circ}\) (since the sum of the arcs in a circle is \(360^{\circ}\), and if one arc is \(130^{\circ}\) and another is \(40^{\circ}\), then \(360-(130 + 40)=170^{\circ}\)).

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

By the inscribed - angle theorem, \(m\angle ABC=\frac{1}{2}m\overset{\frown}{AE}\). So \(m\angle ABC=\frac{1}{2}\times170^{\circ}=85^{\circ}\).

Answer:

D. 85°