Answer:
The measure of the complement angle is [tex]18\°[/tex]
Step-by-step explanation:
Let
x-----> the angle
we know that
The complement of an angle is equal to [tex](90-x)\°[/tex]
The supplement of an angle is equal to [tex](180-x)\°[/tex]
we have
The complement of an angle is one-sixth the measure of the supplement of the angle
[tex](90-x)\°=(1/6)(180-x)\°[/tex]
solve for x
[tex](540-6x)\°=(180-x)\°[/tex]
[tex](6x-x)=(540-180)\°[/tex]
[tex](5x)=(360)\°[/tex]
[tex]x=72\°[/tex]
Find the measure of the complement angle
[tex](90-x)\°[/tex] ------> [tex](90-72)=18\°[/tex]
