Question

what is the measure of $overparen{ac}$? a. $48^{circ}$ b. $138^{circ}$ c. $132^{circ}$ d. $42^{circ}$

Explanation:

Step1: Recall circle - arc relationship

The sum of arcs in a semi - circle is 180°.

Step2: Identify known arcs

We know that arc \(AE\) is composed of arc \(AD\) and arc \(DE\), where arc \(AD = 90^{\circ}\) and arc \(DE=42^{\circ}\).

Step3: Calculate arc \(AC\)

Arc \(AC=180^{\circ}-\text{arc}(DE)\). Since \(\text{arc}(DE) = 42^{\circ}\), then \(\text{arc}(AC)=180 - 42=138^{\circ}\).

Answer:

B. 138°