Transformations and Similarity Unit Test

Question

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Question
△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=
°

Answer 1

Since △CDE∼△PQR, the corresponding angles are congruent. Thus, m∠P = 13° and m∠D = 65°.

To find m∠Q and m∠R, we can use the fact that the sum of the angles in a triangle is 180°.

m∠C + m∠D + m∠E = 180°
13° + 65° + m∠E = 180°
78° + m∠E = 180°
m∠E = 180° - 78°
m∠E = 102°

Since △PQR is similar to △CDE, we can conclude that m∠Q = m∠E = 102°.

Finally, we can find m∠R using the sum of angles in a triangle again.

m∠P + m∠Q + m∠R = 180°
13° + 102° + m∠R = 180°
115° + m∠R = 180°
m∠R = 180° - 115°
m∠R = 65°

Therefore, the measures of angles P, Q, and R are:
m∠P = 13°, m∠Q = 102°, and m∠R = 65°.