Final answer:
The question lacks sufficient detail to determine the measure of angle mq. The given lengths rq and pr need to be contextualized within a geometric figure or theorem to calculate an angle measure.
Step-by-step explanation:
The question seems to be asking for the measure of an angle, denoted here as mq. However, the information provided is insufficient to directly determine an angle measure without additional context, such as a diagram or more details about the geometric shape or theorem involved.
The lengths rq and pr are given, but without knowing how they relate to angle mq, we cannot conclude what the measure of angle mq is. If rq and pr are sides of a triangle that includes angle mq, and if it's a right-angled triangle, then trigonometric ratios could be applied to find the angle.
Otherwise, we need more information, such as the type of polygon, the relationships between the sides and angles, or any relevant theorems that might apply (such as those pertaining to circles, if this is a problem involving chords, for example).
The complete question is: Given RQ = 20 inches and PR = 25 inches what is the m∠Q?