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If an angle of a parallelogram is four fifths of its adjacent angle, find the angles of the parallelogram.

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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.

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