Question

in a cyclic quadrilateral ABCD, angle A is equal to 2 X + 4 degree, angle b is equal to y + 3 degree, angle C is equal to 2y + 10 degree and Angle d is equal to 4 x minus 5 degree find the four angles

Answer 1

in a cyclic quadrilateral sum of opposite angles is 180 degree

A+C=180 and B+C=180

2x+4+2y+10=180

x+y=83

y+3+4x-5=180

4x+y=182

on solving we get

x=33 degree

y=50 degree

A=2*33+4=70 degree

B=50+3=53 degree

C=2*50+10+110 degree

D=4*33-5=127 degree

Answer 2

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