Question

An angle measures 12° less than the measure of its supplementary angleWhat is the measure of each angle?

Answer 1

Supplementary angles add up to 180°.

Assuming the angles are x and y, we have that

`x+y=180\text{ ----------(1)}`

If one angle is 12° less than the other, we have the equation to represent the statement to be

`x-12=y\text{ ----------(2)}`

We can solve both equations 1 and 2 simultaneously.

Let us substitute for y in equation 2 into equation 1:

`\begin{gathered} x+x-12=180 \\ 2x=180+12 \\ 2x=192 \\ x=(192)/(2) \\ x=96 \end{gathered}`

To find y, we can put the value of x into equation 2:

`\begin{gathered} y=x-12 \\ y=96-12 \\ y=84 \end{gathered}`

Therefore, the values for each angle are 84° and 96°