In a cyclic quadrilateral abcd, a=(2X+4)deg,B=(y+30)deg,C=(2y+10)deg,&d=(4x-5)deg then find the measures of each angle of quadrilateral
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in a cyclic quadrilateral sum of opposite angles are supplementary
1)<A +<C =180
2x+4 +2y+10 =180
2x+2y= 180-14
2x+2y =166
x+y =83---(1)
2)<B +<D =180
y+30+4x-5 =180
4x+y = 180-25
4x+y =155---(2)
subtract (1) from (2)
3x= 155-83
3x= 72
x=72/3
x=24
substitute x= 24 in (1)
x+y =83
24+y =83
y=83-24=59
therefore
x= 24, y=59
<A =2x+4 = 2*24+4=52
<B =y+30 =59+30 =89
<C =2y+10 =2*59+10 =128
<D = 4x-5 =4*24 -5 =91
1)<A +<C =180
2x+4 +2y+10 =180
2x+2y= 180-14
2x+2y =166
x+y =83---(1)
2)<B +<D =180
y+30+4x-5 =180
4x+y = 180-25
4x+y =155---(2)
subtract (1) from (2)
3x= 155-83
3x= 72
x=72/3
x=24
substitute x= 24 in (1)
x+y =83
24+y =83
y=83-24=59
therefore
x= 24, y=59
<A =2x+4 = 2*24+4=52
<B =y+30 =59+30 =89
<C =2y+10 =2*59+10 =128
<D = 4x-5 =4*24 -5 =91
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