In this geometry problem, we are determining the measure of angle QOR given the measures of other angles. As per the angle sum property of triangles, the sum of the measures of the three angles of a triangle is always 180°.

The question provides us with the measures of two angles of triangle OQP and ORP. Specifically, we are given that ∠OQP = 30° and ∠ORP = 20°.

Then to calculate ∠POR (or ∠OQR), we subtract ∠OQP from 180°, because these two angles make up a straight line or a linear pair. Thus, ∠POR = 180° - 30° = 150°.

The same logic is used to calculate ∠ROQ, by subtracting ∠ORP from 180°. Thus, ∠ROQ =180° - 20° = 160°.

Angle ∠QOR, which we are seeking, is calculated by subtracting ∠POR and ∠ROQ from 360° (complete angle at a point). We subtract because we are finding the remaining angle. So, ∠QOR = 360° - 150° - 160° = 50°