In the diagram, we are dealing with a circle where $\angle QOR = 42^\circ$, and we are tasked to find $\angle QPR$.

Key Geometry Concept:

• Angle subtended by an arc at the center is twice the angle subtended at any point on the circumference of the circle. This is known as the angle at the center theorem.

Given:

• $\angle QOR = 42^\circ$ (angle at the center).

Using the angle at the center theorem, the angle at the circumference (which is $\angle QPR$) is half of $\angle QOR$: $\angle QPR = \frac{1}{2} \times 42^\circ = 21^\circ$

However, none of the given choices match this value. Let me recheck the options closely.

Ah, there seems to be a common mistake with the interpretation of this problem—assuming the $\angle QPR$ is the direct half of the central angle might be misleading since this type of configuration could be trickier based on the specific location of points $P, Q, R$. We might need to recheck or calculate with alternative geometry approaches. Would you like to recheck manually, or