Question

The measure of an angle's supplement is 44 degrees less than the measure of the angle. What are the measures of the angle and its supplement?

Answer 1

The angle is 112 degrees and the supplement is 68 degrees.

Explanation:

Let the angle’s measure be represented by `x` and the supplement’s measure be represented by `y`.

Since supplementary angles add to 180 degrees,

`x+y=180`

Since the supplement is 44 degrees less than the angle,

`y+44=x`

We can substitute `y+44` for `x` in the first equation, since they are equivalent.

`y+44+y=180`

`2y+44=180`

`2y=136`

`y=68`

Substitute 68 for y in one of the original equations and solve.

`68+44=x`

`x=112`