Question

the sum of the two opposite angles of a parallelogram is 150° find all the angles of the parallelogram

Answer 1

Angle 1 - 150
Angle 2- 150
Angle 3-30
Angle 4-30
Total 360 degree
I hope it helps you......

Answer 2

Let ABCD be the parallelogram.
Given sum of opposite angles, ∠A + ∠C = 150° → (1)
But in a parallelogram, opposite angles are equal
That is ∠A =∠C
Hence equation (1) becomes,
∠A + ∠A = 150°
⇒ 2∠A = 150°
∴ ∠A = 75°
⇒∠C = 75
But sum of adjacent angles in a parallelogram is 180°
That is ∠A + ∠B = 180°
⇒ 75° + ∠B = 180°
∴ ∠B = 105
⇒ ∠D = 105° (Opposite angles are equal in a parallelogram)
Thus ∠A = ∠C = 75° and ∠B = ∠D = 105°