Consider ABCD as a parallelogram
If ∠ A = xo
We know that ∠ B is adjacent to A which can be written as 4/5 xo
Opposite angles are equal in a parallelogram
So we get
∠ A = ∠ C = xo and ∠ B = ∠ D = 4/5 xo
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
x + (4/5) x + x + (4/5) x = 360o
By addition we get
2x + (8/5) x = 360o
By taking the LCM as 5
(18/5) x = 360o
By cross multiplication
x = (360 × 5)/18
On further calculation
x = 100o
By substituting the value of x
So we get
∠ A = ∠ C = x = 100o
∠ B = ∠ D = 4/5 xo = (4/5) (100o) = 80o
Therefore, ∠ A = ∠ C = x = 100o and ∠ B = ∠ D = 80o.