In the following figure, ABCD and PQRS are two parallelograms such that ∠D = 120° and ∠Q = 70°. Find the value of x.

In parallelogram ABCD,

⇒ ∠A = ∠C and ∠B = ∠D = 120° (Opposite angles of a parallelogram are equal)

⇒ ∠A + ∠B + ∠C + ∠D = 360° (By angle sum property)

⇒ ∠C + ∠D + ∠C + ∠D = 360°

⇒ 2∠C + 120° + 120° = 360°

⇒ 2∠C + 240° = 360°

⇒ 2∠C = 360° - 240°

⇒ 2∠C = 120°

⇒ ∠C = $\dfrac{120°}{2}$ = 60°.

In parallelogram PQRS,

⇒ ∠S = ∠Q = 70° (Opposite angles of a parallelogram are equal)

In △ OSC,

By angle sum property of triangle,

⇒ ∠S + ∠C + ∠O = 180°

⇒ 70° + 60° + x = 180°

⇒ 130° + x = 180°

⇒ x = 180° - 130° = 50°.

Hence, x = 50°.