Question

12 in the diagram, rt bisects ∠srq and m∠qrt = 54°. find m∠srq. a 36° b 108° c 54° d 72°

Explanation:

Step1: Recall angle - bisector definition

An angle - bisector divides an angle into two equal parts. So if $RT$ bisects $\angle SRQ$, then $\angle SRT=\angle QRT$.

Step2: Find $\angle SRQ$

Since $\angle QRT = 54^{\circ}$ and $\angle SRQ=\angle SRT+\angle QRT$ and $\angle SRT=\angle QRT$, then $\angle SRQ = 2\times\angle QRT$.
$\angle SRQ=2\times54^{\circ}=108^{\circ}$

Answer:

b. $108^{\circ}$