Question

what is the measure of ∠rst shown in the diagram below? a. 64° b. 68° c. 56° d. 60°

Explanation:

Step1: Recall angle - arc relationship

The measure of an angle formed by two secants is half the positive difference of the measures of the intercepted arcs.

Step2: Identify the arcs

The larger intercepted arc is 153° and the smaller intercepted arc is 25°.

Step3: Calculate the angle measure

\[m\angle{RST}=\frac{1}{2}(153 - 25)=\frac{1}{2}(128)=64^{\circ}\]

Answer:

A. 64°