△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=
To find the measures of angles P, Q, and R, we can use the fact that corresponding angles of similar triangles are congruent.
Since triangle CDE is similar to triangle PQR, we can match up the corresponding angles:
angle P corresponds to angle C
angle Q corresponds to angle D
angle R corresponds to angle E
Given that angle C is 13° and angle D is 65°, we can conclude that:
angle P is also 13°
angle Q is also 65°
To find angle R, we need to find the third angle of triangle CDE. We know that the sum of the angles in a triangle is 180°. So, we can find angle R by subtracting the sum of angles C and D from 180°:
Angle R = 180° - (angle C + angle D)
Angle R = 180° - (13° + 65°)
Angle R = 180° - 78°
Angle R = 102°
Therefore, the measures of angles P, Q, and R are:
m∠P = 13°
m∠Q = 65°
m∠R = 102°.