In a cyclic quadrilateral, the sum of opposite angles is 180° and sum of all the interior angles in a quadrilateral is 360°.

∠A + ∠B + ∠C + ∠D = 360°

⇒ (2x + 4)° + (y + 3)° + (2y + 10)° + (4x - 5)° = 360°

⇒ 6x° + 3y° = 348°

⇒ 2x° + y° = 116°.....(1)

and,

∠A + ∠C = 180°

⇒ 2x° + 2y° = 166°

⇒ x° + y° = 83°.....(2)

Subtracting equation (2) from (1), we get -

⇒ x° = 33°

Substituting the value of x° in equation (2), we get -

y° = 50°

Thus, ∠A = 70°, ∠B = 53°, ∠C = 110°, and ∠D = 127°