Question

what is the measure of ∠rcd in the figure below? a. 35° b. 55° c. 11° d. 60° e. 70° f. cannot be determined

Explanation:

Step1: Identify congruent right - triangles

In right - triangles $\triangle CPD$ and $\triangle CRD$, $CD = CD$ (common side), $PD=RD = 11$, and $\angle CPD=\angle CRD = 90^{\circ}$. By the Hypotenuse - Leg (HL) congruence criterion, $\triangle CPD\cong\triangle CRD$.

Step2: Find the measure of $\angle RCD$

Since $\triangle CPD\cong\triangle CRD$, $\angle RCD=\angle PCD$. Given that $\angle PCD = 35^{\circ}$, then $\angle RCD=35^{\circ}$.

Answer:

A. $35^{\circ}$