Since triangles \( \triangle CDE \) and \( \triangle PQR \) are similar (denoted by \( \triangle CDE \sim \triangle PQR \)), all corresponding angles of the triangles are equal.
Given the angles in triangle \( CDE \):
- \( m\angle C = 13^\circ \)
- \( m\angle D = 65^\circ \)
We can find the measure of angle \( E \) in triangle \( CDE \): \[ m\angle E = 180^\circ - m\angle C - m\angle D = 180^\circ - 13^\circ - 65^\circ = 102^\circ \]
Now, we can find the corresponding angles in triangle \( PQR \):
- Since \( \triangle CDE \sim \triangle PQR \):
- \( m\angle P = m\angle C = 13^\circ \)
- \( m\angle Q = m\angle D = 65^\circ \)
- \( m\angle R = m\angle E = 102^\circ \)
Thus, the measures of the angles in triangle \( PQR \) are:
- \( m\angle P = 13^\circ \)
- \( m\angle Q = 65^\circ \)
- \( m\angle R = 102^\circ \)