Identify the relationship between the angle at the center and the angle at the circumference.

Step 1: Identify the relationship between the angle at the center and the angle at the circumference.
The angle at the center, $\angle POR$, and the angle at the circumference, $\angle PQR$, are both subtended by the same arc PR.

Step 2: Apply the circle theorem.
The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

$$\angle POR = 2 \times \angle PQR$$

Step 3: Substitute the given value and solve for $\angle PQR$.

$$130^\circ = 2 \times \angle PQR$$ $$$$