Question

If four angles of a cyclic quadrilateral are (2x –1)º, (y + 5) ; (2y + 15)º and (4x – 7)º, then​

Answer 1

Step-by-step explanation:

In a cyclic quadrilateral, opposite angles are supplementary.

So, A+C = 180° => 2x-1+2y+15 = 180°

=> 2x+2y +14 = 180 => x+y = 83 …….(1)

Again B + D = 180° => y+5+4x-7= 180

=> 4x +y = 182………………(2)

(2)-(1) gives 3x = 99 => x = 33°=> y = 50° by (1).

So A = 2x-1 = 65°, B = y+5 = 55°, C = 2y+15 = 115° and D = 4x-7 = 125°

Check: A+C = 65°+115° = 180° and

B+D = 55° +125° = 180