Question 147 In parallelogram PQRS, O is the mid-point of SQ. Find ∠S,∠R, PQ, QR and diagonal PR.
Open in App
Solution
Given, ∠RQY=60∘ ∠SRQ=∠RQY [SR∥PY, RQ is the transversal] ⇒∠R=60∘ ∴∠S=180∘−∠R=180∘−60∘=120∘ [∵ adjacent angles are supplementary]
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] PR is bisected by SQ, so PR=2×PO=2×6=12cm