# In a cyclic quadrilateral ABCD, /_ A= (2x+4)° , /_=(y+3)°, /_ C= (2y+10)° and /_D=(4x-5)°.find the measure of each angle.

2
by minal61

2015-03-09T00:20:00+05:30

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As it is a cyclic quadrilateral../_A+/_C=/_B+/_D=180......2x+4+2y+10=180.....2x+2y+14=180...,,x+y+7=90..... x+y=83..eq1.....Now for eq2..y+3+4x-5=180....4x+y-2=180...4x+y=182..y=182-4x NOW SUBSTITUTING THE VALUE OF y..in eq1 we have..x+182-4x=83...-3x=-99...x=33....Again in eq1..x+y=83....33+y=83....y=50..(Ans)
2015-03-09T10:48:39+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
In a cyclic quadrilateral, Opposite angles are supplementary.
angle A + angle C = 180 deg. and also angle B + angle D = 180 deg.

Now 2x + 4 + 2y + 10 = 180 => x+y = 83 deg.
similarly,  y+3+4x-5 = 180 => 4x+y = 182 deg.

solving the two simultaneous equations in x and y we get,
3x = 99 deg;  x= 33 deg
y = 50 deg.

now calculate A,B,C and D.
A = 70 deg    =>  C = 110 deg
B = 53 deg  => D = 127 deg