Question

Two angles are supplementary supplementary if the sum of their measures is 180 degrees .180°. If the measure of an angle is 9 x9x ​degrees, represent the measure of its supplement supplement as an algebraic expression in x.

Answer 1

The answer is
`\beta =180-9x`

Explanation:

Two angles are supplementary if the sum of their measures is 180°. That means that two angles, let's say, α, and its supplement, β, are supplementary if the following is true:

`\alpha +\beta =180\\`

Now, let's say that α measures 9x degrees, and let us replace in the above expression:

`9x +\beta =180\\`

If we now want to represent the measure of the supplementary angle, β, we have to subtract 9x from both sides of the expression to get the final algebraic expression of β in x:

`\beta =180-9x`

Note that an algebraic expression is just a mathematical relationship between numbers and variables! The goal was to isolate the supplementary angle, β, and find its relationship with the variable x.