Question

which expression gives the measure of ∠rst in the diagram below? a. $\frac{1}{2}(162^{circ}+38^{circ})$ b. $\frac{1}{2}(162^{circ}-38^{circ})$ c. $162^{circ}+38^{circ}$ d. $162^{circ}-38^{circ}$

Explanation:

Step1: Recall angle - measure formula

The measure of an angle formed by two secants of a circle is given by $\frac{1}{2}$(the difference of the measures of the intercepted arcs).

Step2: Identify intercepted arcs

The larger intercepted arc is $162^{\circ}$ and the smaller intercepted arc is $38^{\circ}$.

Step3: Calculate the measure of $\angle{RST}$

Using the formula, the measure of $\angle{RST}=\frac{1}{2}(162^{\circ}-38^{\circ})$.

Answer:

B. $\frac{1}{2}(162^{\circ}- 38^{\circ})$