Question

The complement of an angle is one-sixth the measure of the supplement of the angle. What is the measure of the complement angle?

Answer 1

18⁰

Explanation:

Angle = x

Complement = 90 - x

Supplement = 180 - x

Given:

90 - x = 1/6 × (180 - x)

540 - 6x = 180 - x

5x = 360

x = 72

Complement = 90 - 72 = 18⁰

Answer 2

The measure of the complement angle is
`18\°`

Explanation:

Let

x-----> the angle

we know that

The complement of an angle is equal to
`(90-x)\°`

The supplement of an angle is equal to
`(180-x)\°`

we have

The complement of an angle is one-sixth the measure of the supplement of the angle

`(90-x)\°=(1/6)(180-x)\°`

solve for x

`(540-6x)\°=(180-x)\°`

`(6x-x)=(540-180)\°`

`(5x)=(360)\°`

`x=72\°`

Find the measure of the complement angle

`(90-x)\°` ------>
`(90-72)=18\°`