Since triangles \( \triangle CDE \) and \( \triangle PQR \) are similar (denoted as \( \triangle CDE \sim \triangle PQR \)), their corresponding angles are equal.
Given:
- \( m\angle C = 13^\circ \)
- \( m\angle D = 65^\circ \)
To find the measure of angle \( E \) in triangle \( CDE \): \[ m\angle E = 180^\circ - m\angle C - m\angle D \] \[ m\angle E = 180^\circ - 13^\circ - 65^\circ \] \[ m\angle E = 180^\circ - 78^\circ = 102^\circ \]
Now, since the triangles are similar:
- \( m\angle P = m\angle C = 13^\circ \)
- \( m\angle Q = m\angle D = 65^\circ \)
- \( m\angle R = m\angle E = 102^\circ \)
Therefore, the measures of angles \( P \), \( Q \), and \( R \) are:
- \( m\angle P = 13^\circ \)
- \( m\angle Q = 65^\circ \)
- \( m\angle R = 102^\circ \)
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