Let:
x = 1st angle
y = 2nd angle
Since they are supplementary:
[tex]x+y=180_{\text{ }}(1)[/tex]
One is 54 more than 1/2 of the other, so:
[tex]y=\frac{1}{2}x+54_{\text{ }}(2)[/tex]
Replace (2) into (1):
[tex]\begin{gathered} x+\frac{1}{2}x+54=180 \\ \frac{3}{2}x=180-54 \\ \frac{3}{2}x=126 \\ x=\frac{2}{3}\cdot126 \\ x=84 \end{gathered}[/tex]
Replace x into (2):
[tex]\begin{gathered} y=\frac{1}{2}(84)+54 \\ y=42+54 \\ y=96 \end{gathered}[/tex]
Answer:
The two angles are 84⁰ and 96⁰
