Find the angles which is 2/3 of its supplement.

Let the required angle be x°.

Its supplement = (180 − x)°

As per the condition, we get

(2/3) of (180 − x)° = x°

⇒ (2/3) × (180 − x)° = x°

⇒ (2/3) × 180° − (2/3) × x° = x°

⇒ 120° − (2/3)x° = x°

⇒ x° + (2/3)x° = 120°

⇒ (5/3)x° = 120°

∴ x° = 120° × (3/5) = 72°

Thus, the required angle be 72°.