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

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

Solution:

We know that the opposite angles of a cyclic quadrilateral are supplementary.

Hence, sum of the measures of opposite angles in a cyclic quadrilateral is 180°.

Therefore, from the figure shown below,

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

∠A + ∠C = 180°

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

4y + 20 - 4x = 180

- 4( x - y) = 160

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

Also,

∠B + ∠D = 180°

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

3y - 5 - 7x + 5 = 180

-7x + 3y = 180

7x - 3y = - 180 .... (2)

Multiplying equation (1) by 3, we obtain

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

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

(7x - 3y) - (3x - 3y) = - 180 - (- 120)

4x = - 60

x = - 15

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

-15 - y = - 40

y = 25

Therefore, by using x = -15 and y = 25 we have,

∠A = 4y + 20 = 4 × 25 + 20 = 120°

∠B = 3y - 5 = 3 × 25 - 5 = 70°

∠C = - 4x = - 4 × (- 15) = 60°

∠D = - 7x + 5 = - 7 × (- 15) + 5 = 110°

☛ Check: NCERT Solutions Class 10 Maths Chapter 3

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

Summary:

ABCD is a cyclic quadrilateral as shown in the figure, The angles of the cyclic quadrilateral are ∠A = 120°, ∠B = 70°, ∠C = 60°, and ∠D° = 110 respectively.

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