In the given figure, PQRS is a cyclic quadrilateral. What is the measure of the angle PQR if PQ is parallel to SR?

∠P + ∠R = 180° (∵ PQRS is a cyclic quadrilateral)
110° + ∠R = 180°
∠R = 70°
∠R + ∠Q = 180° (supplementary angle)
70° + ∠Q = 180°
∠PQR = 110°
Note:-

In any cyclic quadrilateral if two sides are parallel, then non-parallel sides are also equal in length. This type of quadrilateral is called an isosceles trapezium.
If AB || CD
Then AD = BC and ∠A = ∠B, ∠C = ∠D