Question

In parallelogram PQRS, O is the mid point of SQ. Find ∠S, ∠R, PQ, QR and diagonal PR.

Answer 1

Given, ∠RQY = 60°

∴ ∠RQP = 120°   ...[Linear pair]

∴ ∠S = 120°   ...[∵ Opposite angles are equal in a parallelogram]

By the angle sum property of a quadrilateral,

∠P + ∠R + ∠S + ∠Q = 360°

⇒ ∠P + ∠R + 120° + 120° = 360°

⇒ ∠P + ∠R + 120°

⇒ 2∠P = 120°

⇒ ∠P = 60°   ...[∵ Opposite angles are equal in parallelogram]

⇒ ∠P = ∠R = 60°

Also, SR = 15 cm

∴ PQ = 15 cm   ...[∵ Opposite sides of a parallelogram are equal]

And PS = 11 cm

∴ QR = 11 cm   ...[∵ Opposite sides of a parallelogram are equal]

And PR = 2 × PO

= 2 × 6

= 12 cm  ...[∵ Diagonals of a parallelogram bisect each other]