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

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In parallelogram PQRS, O is the mid-point of SQ. Find

∠ S, ∠ R

, PQ, QR and diagonal PR.

In Parallelogram PQRS, O Is The Mid-point Of SQ. Find ∠S,�...

Answer:
:
Given,

∠ R Q Y = 60^{\circ}

∠ S R Q = ∠ R Q Y

[

S R ∥ P Y

, RQ is the transversal]

\Rightarrow ∠ R = 60^{\circ}

∴ ∠ S = 180^{\circ} - ∠ R = 180^{\circ} - 60^{\circ} = 120^{\circ}

[

∵

adjacent angles are supplementary]
Also, SR = 15 cm

\Rightarrow

PQ = 15 cm [

∵

opposite sides of a parallelogram are equal]
And PS = 11 cm

\Rightarrow

QR = 11 cm [

∵

opposite sides of a parallelogram are equal]
PR is bisected by SQ, so

P R = 2 \times P O = 2 \times 6 = 12 c m

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