Question

if in a cyclic quadrilateral ABCD angle is equal to 5 Y + 5 degree angle b is equal to 4 Y - 4 degree angle C is equal to X + 10 degree and Angle d is equal to 2 X + 4 degree then find the value of its each angle answer answer kya hoga

Answer 1

Hey friend, Here is your answer-
In □ABCD ,
angle A = 5y + 5 , angle B = 4y- 4 , angle C = x+ 10 , angle D = 2x+ 4
Opposite angles of cyclic quadrilateral are supplementary.
Therefore,
angle A + angle C = 180
5y+ 5 + x + 10 =180
5y + x + 15 =180
x + 5y = 165............ (1)

Similarly,
angle B + angle D = 180
4y- 4 + 2x + 4=180
2x + 4y = 180......... (2)

Multiply equation (1) by 2 ,
2x + 10y = 330.......... (3)

Subtract equation 2 from 3 ,
we get : y = 25

Substitute y = 25 in equation 1
x + 5× 25 = 165
x + 125 = 165
x = 40

Angle A = 5y + 5 = 5×25 +5=130°
Angle B = 4y-4= 4×25-4 = 96°
Angle C = x + 10 = 40+10 = 50°
Angle D = 2x+4 = 2×40+4 = 84°

Hope it will help you.
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