△CDE∼△PQR . m∠C=13° , m∠D=65° . What are the measures of angles P , Q , and R ?(2 points)
m∠P =
°, m∠Q =
° and m∠R=
°
We know that corresponding angles of similar triangles are congruent. Therefore,
m∠C = m∠P
13° = m∠P
m∠D = m∠Q
65° = m∠Q
We also know that the sum of the angles in a triangle is 180°. Therefore,
m∠C + m∠D + m∠E = 180°
13° + 65° + m∠E = 180°
78° + m∠E = 180°
m∠E = 102°
Since angles in a triangle add up to 180°:
m∠P + m∠Q + m∠R = 180°
13° + 65° + m∠R = 180°
78° + m∠R = 180°
m∠R = 102°
Therefore,
m∠P = 13°
m∠Q = 65°
m∠R = 102°