Q16 of 29 Page 3

In a cyclic quadrilateral ABCD ∠A = (2x+4)° , B =(y+3)° ,∠C = (2y+10)° ,∠D =(4x–5)° . Find the four angles.

Given: ∠A = (2x+4)°


B =(y+3)°


∠C = (2y+10)°


∠D =(4x–5)°


To find: The values of four angles.


Explanation:



Opposite angles of a cyclic quadrilateral are supplementary.


∠A + ∠C = 180°


∠B + ∠D = 180°


For given angles.


2x + 4 + 2y + 10 = 180


⇒ x + y = 83 ……(1)


y + 3 + 4x – 5 = 180


⇒ y + 4x = 182 ……(2)


(1) – (2)


⇒ x – 4x = 83 – 182


⇒ x = 33°


Thus, y = 50°


∠A = 2x + 4 = 70°


∠B = y + 3 = 53°


∠C = 2y + 10 = 110°


∠D = 4x – 5 = 127°


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