IN A CYCLIC QUADEILATERAL ABCD ANGLE A=(X+2Y+7), ANGLE B=(2X+Y+7), ANGLE C=(4X+Y+3),ANGLE D= (4X+8).FIND THE FOUR ANGLE

Asked by kalyani semwal | 19th Apr, 2013, 06:26: PM

Expert Answer:

In a cyclic quadrilateral, the sum of opposite angles is equal to 180
 
Hence, angle A + angle C = 180
x+2y+7 + 4x+y+3 = 180
5x+3y = 170
 
Also, angle B + angle D = 180
2x+y+7 + 4x+8 = 180
6x+y= 165
y = 165-6x
 
Substituting in the first equation
5x+3(165-6x) = 170
495-13x = 170
x = 25
 
y = 165 - 6(25)  = 15
 
Hence, angle A = 62
angle B = 72
angle C = 118
Angle D =108
 

Answered by  | 19th Apr, 2013, 06:54: PM

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