Q. 55.0( 1 Vote )

In a cyclic

Answer :


Cyclic Quadrilateral according to the question is shown above.


Now by property of cyclic quadrilateral, we know that opposite angles of a cyclic quadrilateral are supplementary.


Therefore,


Sum of Adjacent angles of cyclic quadrilateral = 180°


So, we have,


(2x + 4) + (2y + 10) = 180°


2x + 2y = 166°…..(i)


And also,


(y + 3) + (4x – 5) = 180°


4x +y = 182° ……..(ii)


Solving equations (i) and (ii)


Eq (i) – 2 × eq (ii)


2x + 2y – 8x – 2y = 166° – 364°


–6x = – 198°


x = 33°


Putting the value of x in eq (i) we get,


2x + 2y = 166°


2 × 33° + 2y = 166°


2y = 100°


y = 50°


Now each angle of the cyclic quadrilateral is,


A = (2x + 4)° = 2 × 33° + 4° = 70°


B = (y + 3)° = 50° + 3° = 53°


C = (2y + 10)° = 2 × 50° + 10° = 110°


D = (4x – 5)° = 4 × 33° – 5° = 127°


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