Since △CDE is similar to △PQR (denoted as △CDE ∼ △PQR), the corresponding angles of the triangles are equal.
Given:
- m∠C = 13°
- m∠D = 65°
To find m∠E, we use the fact that the sum of angles in a triangle is 180°:
\[ m∠E = 180° - m∠C - m∠D \] \[ m∠E = 180° - 13° - 65° \] \[ m∠E = 180° - 78° = 102° \]
Now, we can match the angles of △CDE with △PQR:
- m∠C = m∠P
- m∠D = m∠Q
- m∠E = m∠R
Thus, we have:
- m∠P = m∠C = 13°
- m∠Q = m∠D = 65°
- m∠R = m∠E = 102°
So the measures of the angles in triangle PQR are:
- m∠P = 13°
- m∠Q = 65°
- m∠R = 102°
Final answers:
- m∠P = 13°
- m∠Q = 65°
- m∠R = 102°