Question

Find x, y and z in the following figure where PQRS is a parallelogram.​

Answer 1

Answer:

x = 40°, y = 110°

Step-by-step explanation:

To find x, we need to find ∠RPQ

Using property - the sum of angles on the same side of the transversal = 180°

⇒ ∠PQR + ∠SPQ = 180°

∵ ∠SPQ = ∠SPR + ∠RPQ

∴ ∠PQR + ∠SPR + ∠RPQ = 180°

∠PQR = 110°, ∠SPR = 30°

Let m∠RPQ = k°

⇒ k + 30 + 110 = 180°

⇒ k + 140 = 180°

⇒ k = 180° - 140° = 40°

∴ ∠RPQ = 40°

∵ ∠x and ∠RPQ are alternate interior angles

∴ ∠x = ∠RPQ

∴ ∠x = 40°

Using property - Opposite angles in a parallelogram are equal we can find ∠y.

i.e.

∠y i.e. ∠PSR = ∠RQP

∠RQP = 110°

∵ ∠y i.e. ∠PSR = ∠RQP

∴ ∠Y = 110

Hope it helps...