Question

in a cylcis quadrilateral ABCD, angle A =(2x+4), angle b =(y+3), angel c =(2y+10) and angle d=(4x-5). find the four angles​

Answer 1

Answer:

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

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