To solve for \( m \angle PQR \), we can use the information given about the angles in triangle PQR.
We know:
- \( m \angle PQS = 79^\circ \)
- \( m \angle SQR = 32^\circ \)
To find \( m \angle PQR \), we can use the fact that the sum of angles in triangle PQS is \( 180^\circ \):
\[ m \angle PQS + m \angle SQR + m \angle PQR = 180^\circ \]
Substituting the known values into the equation:
\[ 79^\circ + 32^\circ + m \angle PQR = 180^\circ \]
Now, adding the angles on the left side:
\[ 111^\circ + m \angle PQR = 180^\circ \]
Next, we will isolate \( m \angle PQR \):
\[ m \angle PQR = 180^\circ - 111^\circ \]
\[ m \angle PQR = 69^\circ \]
Thus, the measure of angle \( PQR \) is \( \boxed{69^\circ} \).