Question

In the given figure, AC || PQ and AB || RS, then find ∠y. Also give reasons in support of your answer.

Answer 1

PQ || AC ( given)

∠y = ∠BAC (alt. angles) …(i)

Again AB || RS (given)

∠BAC = ∠LMC …(ii) (corresponding angles)

From (i) and (ii), we get

∠LMC = ∠y

In ΔLMC, exterior angle is equal to sum of opposite interior angles

⇒ 80° = ∠y + 30°

⇒ ∠y = 80° – 30°

⇒ ∠y = 50°