Question

the sum of two opposite angles f a parallelogram is 160 º.find all the angles.

Answer 1

Let ABCD be the parallelogram.
Given sum of opposite angles, ∠A + ∠C = 160° → (1)
But in a parallelogram, opposite angles are equal
That is ∠A =∠C
Hence equation (1) becomes,
∠A + ∠A = 160°
⇒ 2∠A = 160°
∴ ∠A = 80°
⇒∠C = 80°
But sum of adjacent angles in a parallelogram is 180°
That is ∠A + ∠B = 180°
⇒ 80° + ∠B = 160°
∴ ∠B = 100°
⇒ ∠D = 100° (Opposite angles are equal in a parallelogram)
Thus ∠A = ∠C = 80°  and ∠B = ∠D = 100°