Question

If the supplement of an angle is two-third of itself. Determine the angle and its supplement.

Answer 1

Given that

Supplementary of an angle = `2/3`    of angle itself.

The angle measured be ‘x’ say.

Supplementary angle of x will be (180 - x)°

It is given that

(180 - x)° = `2/3` x°

⇒ 180° - x° = `2/3` x°

⇒  `2/3` x° + x° = 180° 

⇒ 2x° + 3x° = 3 × 180°

⇒  5x° = 540°

⇒ x = 108°

Hence, supplement =180 -108 = 72°

∴ Angle will be 108° and its supplement will be 72°.