Answer :

In a cyclic quadrilateral, the sum of opposite angles is 180° and sum of all the interior angles in a quadrilateral is 360°.


A + B + C + D = 360°


(2x + 4)° + (y + 3)° + (2y + 10)° + (4x - 5)° = 360°


6x° + 3y° = 348°


2x° + y° = 116°.....(1)


and,


A + C = 180°


2x° + 2y° = 166°


x° + y° = 83°.....(2)


Subtracting equation (2) from (1), we get -


x° = 33°


Substituting the value of x° in equation (2), we get -


y° = 50°


Thus, A = 70°, B = 53°, C = 110°, and D = 127°


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