Recall that the supplementary angles sum to 180°
Let x and y are the two angles, so we can write
[tex]x+y=180\degree\quad eq.1[/tex]
We are given that the difference of the two supplementary angles is 8°
So we can write
[tex]\begin{gathered} x-y=8\degree \\ x=8\degree+y\quad eq.2 \end{gathered}[/tex]
Substitute eq.2 into eq.1
[tex]\begin{gathered} x+y=180\degree \\ (8\degree+y)+y=180\degree \\ 8\degree+2y=180\degree \\ 2y=180\degree-8\degree \\ 2y=172\degree \\ y=\frac{172\degree}{2} \\ y=86\degree \end{gathered}[/tex]
So, one angle is 86°, the other angle is
[tex]\begin{gathered} x=8\degree+y \\ x=8\degree+86\degree \\ x=94\degree \end{gathered}[/tex]
Therefore, the measure of the two angles is
86°, 94°
