# ABCD is a cyclic

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

⇒4y + 20 - 4x = 180

⇒- 4x + 4y = 160

⇒x - y = - 40   ....(i)

Also, B + D = 180

⇒3y - 5 - 7x + 5 = 180

⇒- 7x
+ 3y = 180   .... (ii)

Multiplying equation (i) by 3, we obtain 3x - 3y = - 120.... (iii)

Adding equations (ii) and (iii), we obtain

- 7x + 3x = 180 - 120

- 4x = 60

x = -15

By using equation (i), we obtain x - y = - 40

-15 - y = - 40

y = -15 + 40

= 25

A = 4y + 20

= 4(25) + 20

∠A= 120°

∠ B = 3y - 5

= 3(25) - 5

∠B= 70°

C = - 4x

= - 4(- 15)

∠C = 60°

∠D = - 7x + 5
= - 7(-15) + 5

= 105 + 5
∠D = 110°

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