Find the angles which is 1/5 of its complement.

Let the required angle be x°.

Its complement = (90 − x)°

As per condition, we get

(1/5) of (90 − x)° = x°

⇒ (1/5) × (90 − x)° = x°

⇒ (1/5) × 90° − (1/5) × x° = x°

⇒ 18° − (1/5)x° = x°

⇒ x° + (1/5)x° = 18°

⇒ (6/5)x° = 18°

∴ x° = 18 × (5/6) = 15°

Thus, the required angle be 15°.