In a parallelogram PQRS, ∠P and ∠Q are in the ratio 1:2. Find the measure of ∠Q.

As we know, the adjacent angles in a parallelogram are supplementary.

In parallelogram PQRS, ∠P and ∠Q are adjacent to each other.

Let ∠P = x and ∠Q = 2x      [Since, ∠P : ∠Q = 1 : 2]

Therefore, ∠P + ∠Q = 180^o

⇒ x + 2x = 180^o

⇒ 3x = 180^o

⇒ x = 60^o

Therefore, ∠Q = 2x = 2 × 60^o = 120^o