Which of the following is the measure of angle rcp?

From the information provided we have:

PD ≅ RD (= 11)

∠CPD ≅ ∠CRD (= 90°)

They both have CD as the hypotenuse.

=> ΔCPD ≅ ΔCRD

=> ∠PCD ≅ ∠RCD

Now we know that:

∠RCP = ∠PCD + ∠RCD

∠RCP = 2 · ∠RCD

∠RCP = 2 · 33° = 66°

So the answer is B

B. 66°

Step-by-step explanation:

In then figure figure , we consider two triangle ΔPCD and Δ RCD in which

∠P ≅ ∠R = 90°

PD≅RD =11

CD≅CD   [Reflexive Property]

Hence, By HL theorem we have

ΔPCD ≅ Δ RCD

[ HL theorem says that if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of other right triangle, then the triangles are said to be congruent.]

Now , By CPCTC we have

∠PCD≅∠RCD

Then , ∠RCP = 33°+33°=66°