△CDE∼△PQR . m∠C=13° , m∠D=65° . What are the measures of angles P , Q , and R ?
We know that corresponding angles of similar triangles are equal. Therefore, ∠C ≅ ∠P, and ∠D ≅ ∠Q.
We are given that ∠C = 13° and ∠D = 65°. Therefore, ∠P = 13° and ∠Q = 65°.
Since the sum of interior angles in a triangle is always 180°, we can find ∠R.
∠C + ∠D + ∠R = 180°
13° + 65° + ∠R = 180°
78° + ∠R = 180°
∠R = 180° - 78°
∠R = 102°
Therefore, ∠P = 13°, ∠Q = 65°, and ∠R = 102°.