△CDE∼△PQR. m∠C=13°, m∠D=65°. What are the measures of angles P, Q, and R?(2 points)
Angle P: 13°
Angle Q: 65°
Angle R: 102°
To find the measures of angles P, Q, and R, we can use the fact that corresponding angles in similar triangles are equal.
In the given triangles △CDE and △PQR, we know that ∠C = 13° and ∠D = 65°.
Since the triangles are similar, this means that the corresponding angles are equal. Therefore:
∠C = ∠P
∠D = ∠Q
So, we can substitute the given angle measures into these equations:
∠P = 13°
∠Q = 65°
To find the measure of angle R, we can use the fact that the sum of interior angles in any triangle is 180°. Therefore:
∠R = 180° - ∠P - ∠Q
Substituting the known angle measures:
∠R = 180° - 13° - 65°
∠R = 180° - 78°
∠R = 102°
So, the measures of angles P, Q, and R are:
∠P = 13°
∠Q = 65°
∠R = 102°