Question

find the angle whose complement is one third of its supplement

Answer 1

Let the angle be x complement of x is (90 − x)° supplement of x is (180 − x)° Given (90 − x)° = (1/3) × (180 − x)° ⇒ 270° − 3x = 180°− x ⇒ 270° − 180° = 3x − x ⇒ 2x = 90° ∴ x = 45°

Answer 2

Answer:

Let the angle be x complement of x is (90 − x)° supplement of x is (180 − x)° Given (90 − x)° = (1/3) × (180 − x)° ⇒ 270° − 3x = 180°− x ⇒ 270° − 180° = 3x − x ⇒ 2x = 90° ∴ x = 45°