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