# ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic quadrilateral

**Solution:**

Pairs of opposite angles of a cyclic quadrilateral are supplementary.

We know that the sum of the measures of opposite angles in a cyclic quadrilateral is 180°. Therefore,

∠A + ∠C = 180°

(4 y + 20) + (- 4x) = 180 4 y + 20 - 4x = 180

-4( x - y) = 160

x - y = -40 ....(1)

And,

∠B + ∠D = 180°

(3y - 5) + (- 7x + 5) = 180

3y - 5 - 7x + 5 = 180

-7x + 3y = 180

7x - 3y = - 180

Multiplying equation (1) by 3, we obtain

3x - 3y = - 120 ....(4)

Subtracting equation (3) from equation (2), we obtain

4x = - 60

x = - 15

Substituting x = - 15 in equation (1), we obtain

-15 - y = - 40

y = 25

Therefore,

∠A = 4 × 25 + 20 = 120°

∠B = 3 × 25 - 5 = 70°

∠C = - 4 × (- 15) =-60°

∠D = - 7 × (- 15) + 5 = 110°

**Video Solution:**

## ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic quadrilateral

### Class 10 Maths NCERT Solutions - Chapter 3 Exercise 3.7 Question 8:

ABCD is a cyclic quadrilateral (see Fig. 3.7). Find the angles of the cyclic quadrilateral

The angles of cyclic quadrilateral for the above image are A = 120, B = 70, C = 60, D = 110.