In a cyclic quadrilateral ABCD∠A = (2x + 4)°∠B = (y + 3)°∠C =

1.	In a cyclic quadrilateral ABCD∠A = (2x + 4)°∠B = (y + 3)°∠C = (2y + 10)°∠D = (4x - 5)°Find the four angles.
Answer» Opposite angles of a cyclic quadrilateral are supplementary ∠A + ∠C = 180° ∠B + ∠D = 180° Given, ∠A = (2x + 4)° ∠B = (y + 3)° ∠C = (2y + 10)° ∠D = (4x - 5)° 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°

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

Answer»

Opposite angles of a cyclic quadrilateral are supplementary

∠A + ∠C = 180°

∠B + ∠D = 180°

Given,

∠A = (2x + 4)°

∠B = (y + 3)°

∠C = (2y + 10)°

∠D = (4x - 5)°

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°