Question

Two angles are making a linear pair. If one of them is one-third of the other, find the angles.

Answer 1

Let one angle be x. It is given that other angle is one-third of first.

So, other angle will be `1/3 x`.

Again, given that both the angles are making a linear pair.

So, their sum will be 180°.

∴ `x + 1/3 x` = 180°

⇒ `(3x + x)/3` = 180°  ......[Taking LCM of 1 and 3 on LHS]

⇒ `(4x)/3` = 180°

⇒ x = `(180^circ xx 3)/4`

⇒ x = 135°

Hence, the angles are 135° and `1/3` × 135°, i.e. 135° and 45°.