Find an angle which is one-fifth of its supplement.

Let the angle be x.

Its supplement is (180° - x).

The problem states the angle is $\dfrac{1}{5}$ of its supplement.

∴ x = $\dfrac{1}{5}(180^{\circ} - x)$

⇒ 5x = 180° - x

⇒ 5x + x = 180°

⇒ 6x = 180°

⇒ x = $\dfrac{180^{\circ}}{6}$

⇒ x = 30°

Hence, the required angle measures 30°.