Consider ABCD as a parallelogram
Let us take ∠ A as the smallest angle
So we get
∠ B = 2 ∠ A – 30o
We know that the opposite angles are equal in a parallelogram
∠ A = ∠ C and ∠ B = ∠ D = 2 ∠ A – 30o
We know that the sum of all the angles of a parallelogram is 360o
It can be written as
∠ A + ∠ B + ∠ C + ∠ D = 360o
By substituting the values in the above equation
∠ A + (2 ∠ A – 30o) + ∠ A + (2 ∠ A – 30o) = 360o
On further calculation
∠ A + 2 ∠ A – 30o + ∠ A + 2 ∠ A – 30o = 360o
So we get
6 ∠ A – 60o = 360o
By addition
6 ∠ A = 360o + 60o
6 ∠ A = 420o
By division
∠ A = 70o
By substituting the value of ∠ A
∠ A = ∠ C = 70o
∠ B = ∠ D = 2 ∠ A – 30o = 2 (70o) – 30o
∠ B = ∠ D = 110o
Therefore, ∠ A = ∠ C = 70o and ∠ B = ∠ D = 110o.