Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.

Solution:

Given, both the pairs of opposite angles of a quadrilateral are equal and supplementary.

We have to find the measure of each angle.

Consider a quadrilateral ABCD,

Given, ∠A = ∠C and ∠B = ∠D

Also, ∠A + ∠C = 180°

Now, ∠A + ∠A = 180°

2∠A = 180°

∠A = 180°/2

∠A = 90°

Similarly, ∠B + ∠D = 180°

Now, ∠B + ∠B = 180°

2∠B = 180°

∠B = 180°/2

∠B = 90°

Therefore, each angle is equal to 90 degrees.

✦ Try This: Find the measure of each angle of a regular nonagon.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 166

Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.

Summary:

Both the pairs of opposite angles of a quadrilateral are equal and supplementary. The measure of each angle is 90 degrees.

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