Respuesta :
Supplementary angles add up to 180°.
Assuming the angles are x and y, we have that
[tex]x+y=180\text{ ----------(1)}[/tex]If one angle is 12° less than the other, we have the equation to represent the statement to be
[tex]x-12=y\text{ ----------(2)}[/tex]We can solve both equations 1 and 2 simultaneously.
Let us substitute for y in equation 2 into equation 1:
[tex]\begin{gathered} x+x-12=180 \\ 2x=180+12 \\ 2x=192 \\ x=\frac{192}{2} \\ x=96 \end{gathered}[/tex]To find y, we can put the value of x into equation 2:
[tex]\begin{gathered} y=x-12 \\ y=96-12 \\ y=84 \end{gathered}[/tex]Therefore, the values for each angle are 84° and 96°
