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

Answer:

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

Step-by-step 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

$(90-x)\°$ ------> $(90-72)=18\°$

Answer 2

Answer:

18⁰

Step-by-step 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