Since triangle CDE is similar to triangle PQR, the corresponding angles are equal.
Given:
- \( m∠C = 13^\circ \)
- \( m∠D = 65^\circ \)
To find \( m∠E \), we can use the fact that the sum of the angles in a triangle is \( 180^\circ \):
\[ m∠E = 180^\circ - m∠C - m∠D = 180^\circ - 13^\circ - 65^\circ = 102^\circ \]
Now, since triangle CDE is similar to triangle PQR, the corresponding angles are:
- \( m∠P = m∠C = 13^\circ \)
- \( m∠Q = m∠D = 65^\circ \)
- \( m∠R = m∠E = 102^\circ \)
Thus, the measures of angles P, Q, and R are:
- \( m∠P = 13^\circ \)
- \( m∠Q = 65^\circ \)
- \( m∠R = 102^\circ \)