In the given figure, ABCD is a trapezium in which ∠A = (x + 25)°, ∠B = y°, ∠C = 95° and ∠D = (2x + 5)°. Find the values of x and y.

We know that,

Sum of adjacent co-interior angles of a trapezium = 180° (As AB || DC)

∴ ∠A + ∠D = 180°

⇒ (x + 25)° + (2x + 5)° = 180°

⇒ 3x° + 30° = 180°

⇒ 3x° = 180° - 30°

⇒ 3x° = 150°

⇒ x° = 50°

⇒ x = 50.

Sum of adjacent co-interior angles of a trapezium = 180° (As AB || DC)

∴ ∠C + ∠B = 180°

⇒ 95° + y° = 180°

⇒ y° = 180° - 95°

⇒ y° = 85°

⇒ y = 85.

Hence, x = 50, y = 85.