Question

what is the measure of ∠abc? 131° 53° a. 127° b. 88° c. 131° d. 92°

Explanation:

Step1: Recall the vertical - angles and arc - angle relationship

The measure of an angle formed by two intersecting chords in a circle is half the sum of the measures of the intercepted arcs.

Step2: Identify the intercepted arcs

The arcs intercepted by ∠ABC are arc AC and arc DE. The measure of arc AC = 53° and the measure of arc DE=131°.

Step3: Apply the formula

The measure of ∠ABC=$\frac{1}{2}$(measure of arc AC + measure of arc DE). Substitute the values: $\frac{1}{2}(53 + 131)=\frac{1}{2}(184)=92^{\circ}$.

Answer:

D. 92°