Question

question 9 of 10 what is the measure of ∠spq in the figure below? a. 14° b. 62° c. 56° d. 28° e. 15° f. cannot be determined

Explanation:

Step1: Identify congruent right - triangles

Triangles $\triangle PSR$ and $\triangle PQR$ are right - triangles with $PS = PQ=10$ and $PR$ is common. By the Hypotenuse - Leg (HL) congruence criterion for right - triangles, $\triangle PSR\cong\triangle PQR$.

Step2: Find the angle measure

Since $\triangle PSR\cong\triangle PQR$, $\angle SPR=\angle QPR$. Given $\angle QPR = 28^{\circ}$, then $\angle SPQ=\angle SPR+\angle QPR$. So $\angle SPQ = 2\times28^{\circ}=56^{\circ}$.

Answer:

C. $56^{\circ}$