Answer:
The angle asked for is 36 degrees, The supplementary angle is 144 degrees.
Step-by-step explanation:
First, set up the problem algebraically. I am using variable "[tex]n[/tex]" to represent the supplementary angle and the variable "[tex]x[/tex]" to represent the the angle asked for.
Since supplementary angles are always angles that add up to 180 degrees, the equation would be:
[tex]x+n=180[/tex]
Since the known angle is 108 degrees less than the supplementary angle, [tex]x[/tex] can also be expressed as [tex]n-108[/tex].
So the equation now looks like this:
[tex](n-108)+n=180[/tex]
Now, solve algebraically.
[tex](n-108)+n=180[/tex]
[tex]2n-108=180[/tex]
[tex]2n=288[/tex]
[tex]n=144[/tex]
Once you have solved algebraically, you would know that the supplementary angle is 144 degrees. To find the other angle, simply subtract 144 from 180.
[tex]180-144=36[/tex]
To double check, subtract 36 from 144. You should get 108.
[tex]144-36=108[/tex]
