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°.

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