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

Pls try to help me out

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by minal61

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Pls try to help me out

by minal61

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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

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