# ABCD is a parallelogram. Points P and Q are taken on the sides AB and AD respectively and the parallelogram PRQA is formed. If ∠C = 45°, find ∠R.

**Solution:**

Given, ABCD is a __parallelogram__.

Points P and Q are taken on the sides AB and AD respectively.

The parallelogram PRQA is formed.

Given, ∠C = 45°

We have to find ∠R.

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

So, ∠A = ∠C = 45°

Since PRQA is a parallelogram, the opposite angles are equal.

So, ∠R = ∠A

Therefore, ∠R = 45°

**✦ Try This:** In a parallelogram ABCD. Its diagonals intersect at point O. If OA = 6 cm and OB = 7.5 cm, find the lengths of AC and BD.

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

**NCERT Exemplar Class 8 Maths Chapter 5 Problem 180**

## ABCD is a parallelogram. Points P and Q are taken on the sides AB and AD respectively and the parallelogram PRQA is formed. If ∠C = 45°, find ∠R.

**Summary:**

ABCD is a parallelogram. Points P and Q are taken on the sides AB and AD respectively and the parallelogram PRQA is formed. If ∠C = 45°, ∠R = 45°.

**☛ Related Questions:**

- In parallelogram ABCD, the angle bisector of ∠A bisects BC. Will angle bisector of B also bisect AD? . . . .
- A regular pentagon ABCDE and a square ABFG are formed on opposite sides of AB. Find ∠BCF
- Find maximum number of acute angles which a convex, a quadrilateral, a pentagon and a hexagon can ha . . . .

Math worksheets and

visual curriculum

visual curriculum