ABCD is a cyclic quadrilateral
if. Angle A = 2x+4
Angle B= x+10
Angle C = 4y+4
Angle D = 5y+5
Find x,y

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Solution

We know that the opposite angles of a cyclic quadrilateral are supplementary, therefore,
∠A + ∠C = 180°
=> 2x+4 + 4y + 4 = 180
=> 2x + 4y = 172......(1) Dividing by 2
=> x +2y= 86

and ∠B + ∠D = 180°
=> x+10 + 5y + 5 = 180
=> x +5y = 165....(2)

(2) -(1) => 3y = 79
y= 79/3 = 26.3
Substituting y= 79/3 in (1)
We get x = 33.3

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ABCD is a cyclic quadrilateral if. Angle A = 2x+4 Angle B= x+10 Angle C = 4y+4 Angle D = 5y+5 Find x,y

ABCD is a cyclic quadrilateral
if. Angle A = 2x+4
Angle B= x+10
Angle C = 4y+4
Angle D = 5y+5
Find x,y