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Question

In a cyclic quadrilateral ABCD,3A=(x+7)o.3B=(y+8)o.3C=(3y+23)o and 3D=(4x+12)o. Find all four angle of the cyclic quadrilateral.

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Solution

ABCD is cyclic quadrilateral
we know
A+C=180 ………….(1)
B+O=180 …………..(2)
Equation (1)
x+7+3y+23=180
x+3y=150 ............(3)
Equation (4)
y+8+4x+12=180
4x+y=160 …………(4)
Solve 3 & 4
4x+12y=600
4x+y=160
_______________
11y=440
_______________
y=40
x+40=160
4x=120
x=30
So
A=x+7=30+7=37
B=y+8=40+8=48
C=3y+23=3×40+23=143
D=4x+12=4×30+12=132.

1259901_1056803_ans_c5f3f49932734bb08b3a13624a0e8573.png

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