Question

The angle whose supplement is three times the complement is __________.

Answer 1

Let the measure of angle be x.

Supplement of the angle = 180º − x

Complement of the angle = 90º − x

It is given that,

Supplement of the angle = 3 × Complement of the angle

⇒ 180º − x = 3(90º − x)

⇒ 180º − x = 270º − 3x

⇒ 3x − x = 270º − 180º

⇒ 2x = 90º

⇒ x = $\frac{90°}{2}$ = 45º

The angle whose supplement is three times the complement is ____45º____.