Question

In a parallelogram ABCD, if ∠ A = (2x + 25)° and ∠ B = (3x – 5)°, find the value of x and the measure of each angle of the parallelogram.

Answer 1

We know that the opposite angles are equal in a parallelogram

Consider parallelogram ABCD

So we get

∠ A = ∠ C = (2x + 25) ^o

∠ B = ∠ D = (3x – 5) ^o

We know that the sum of all the angles of a parallelogram is 360^o

So it can be written as

∠ A + ∠ B + ∠ C + ∠ D = 360^o

By substituting the values in the above equation

(2x + 25) + (3x – 5) + (2x + 25) + (3x – 5) = 360^o

By addition we get

10x + 40^o = 360^o

By subtraction

10x = 360^o – 40^o

So we get

10x = 320^o

By division we get

x = 32^o

Now substituting the value of x

∠ A = ∠ C = (2x + 25) ^o = (2(32) + 25) ^o

∠ A = ∠ C = (64 + 25) ^o

By addition

∠ A = ∠ C = 89^o

∠ B = ∠ D = (3x – 5) ^o = (3(32) – 5) ^o

∠ B = ∠ D = (96 – 5) ^o

By subtraction

∠ B = ∠ D = 91^o

Therefore, x = 32^o, ∠ A = ∠ C = 89^o and ∠ B = ∠ D = 91^o.