△CDE∼△PQR . m∠C=13° , m∠D=65° . What are the measures of angles P , Q , and R ?

Question

m∠P = ___°, m∠Q = ___° and m∠R = ___°

Answer 1

First, we can find the measure of angle E in triangle CDE since angle E is supplementary to angle D.

m∠D + m∠E = 180°
65° + m∠E = 180°
m∠E = 180° - 65°
m∠E = 115°

Now, we can use the angle-angle similarity criterion to find the corresponding angles in triangle PQR since triangle CDE is similar to triangle PQR.

m∠C corresponds to m∠P
m∠D corresponds to m∠Q
m∠E corresponds to m∠R

Therefore:
m∠P = 13°
m∠Q = 65°
m∠R = 115°

So, the measures of angles P, Q, and R are:
m∠P = 13°
m∠Q = 65°
m∠R = 115°