Question

if the sum of pair of opposite angles of parellogram is 200°, find the angles of parellogram

Answer 1

Answer: 100°,80°, 100° & 80°

Step-by-step explanation:

See the parallelogram ABCD in the picture.

Given sum of opposite angles, ∠A + ∠C = 200°

→ (1) But in a parallelogram, opposite angles are equal

That is ∠A =∠C

Hence equation (1) becomes,

∠A + ∠A = 200°

⇒ 2∠A = 200°

∴ ∠A = 100°

⇒∠C = 100°

But sum of adjacent angles in a parallelogram is 180°

That is ∠A + ∠B = 180°

⇒ 100° + ∠B = 180°

∴ ∠B = 80°

⇒ ∠D = 100° (Opposite angles are equal in a parallelogram)

Thus ∠A = ∠C = 100° and ∠B = ∠D = 80°