Question

In a parallelogram ABCD ∠C = 98°. Find ∠A and ∠B.

Answer 1

ABCD is a parallelogram
∠C = 98°
∴ ∠A = ∠C = 98°  ....(opposite angles of a parallelogram are equal)
∠A + ∠B +∠C + ∠D = 360°   ....(Sum of all angles of a quadrilateral = 360°)
98° + ∠B + 98° + ∠D = 360°
∠B + 196 + ∠D = 360°
∠B + ∠D = 360° - 196°
∠B +∠D = 164°
But ∠B = ∠D  ....(opposite angles of a parallelogram are equal)
⇒ 2∠B = 164°
⇒ ∠B = 82° = ∠D
Therefore,
∠B = 82°, ∠A = 98°.