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

**Solution:**

Given, PQRS is a parallelogram.

O is the midpoint of SQ

We have to find ∠S, ∠R, PQ, QR and __diagonal__ PR.

Given, ∠RQY = 60°

Since SR || PY with RQ as transversal, the __corresponding angles__ are equal.

∠SRQ = ∠RQY

So, ∠SRQ=60°

i.e., ∠R=60°

We know that the adjacent angles in a __parallelogram__ are supplementary.

So, ∠PSR + ∠SRQ =180°

∠PSR + 60° = 180°

∠PSR = 180° - 60°

So, ∠PSR = 120°

i.e., ∠S = 120°

Given, SR = 15 cm

We know that the opposite sides of a parallelogram are equal.

So, SR = PQ

PQ = 15 cm

Similarly, PS = QR

QR = 11 cm

From the figure,

We observe that PR is bisected by SQ.

So, PR = 2 × PO

= 2 × 6

= 12 cm

Therefore, the diagonal PR is 12 cm.

**✦ Try This: **In Rhombus PQRS, O is the mid point of SQ. Find ∠S, ∠R, PQ, QR and diagonal PR

**☛ Also Check: **NCERT Solutions for Class 8 Maths

**NCERT Exemplar Class 8 Maths Chapter 5 Problem 147**

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

**Summary:**

In parallelogram PQRS, O is the midpoint of SQ. The values of ∠S, ∠R, PQ, QR and diagonal PR are 120°, 60°, 15 cm, 11 cm and 12 cm.

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