ABCD is a cyclic quadrilateral such that angle A = (4y+20)^o ,angle B =(3y - 5)^o , angle C= (-4x)^o and angle D=(7x + 5)^o .

Find the four angles

plz explain the answer also

Given: ABCD is a cyclic quadrilateral with

∠A = (4y + 20)°, ∠B = (3y – 5)°, ∠C = (4x)°, ∠D = (7x + 5)°.

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

⇒ ∠A + ∠C = 180°

⇒ 4y + 20 + 4x = 180°

⇒ 4 (x + y) = 180° – 20 = 160

⇒ x + y = 40°  ...  (1)

and ∠B + ∠D = 180°

⇒ 3y – 5 + 7x + 5 = 180°

⇒ 7x + 3y = 180° ...  (2)

from (1) and (2) we get

x = 15 and y = 25

Hence ∠A = (4 × 25 + 20)° = 120°

∠B = (3 × 25 – 5)° = 70°

∠C = (4 × 15)° = 60°

∠D = (7 × 15 + 5)° = 110°