Question

Two angles are supplementary if the sum of their measures is 18

Answer 1

Let:

x = 1st angle

y = 2nd angle

Since they are supplementary:

$x+y=180_{\text{ }}(1)$

One is 54 more than 1/2 of the other, so:

$y=\frac{1}{2}x+54_{\text{ }}(2)$

Replace (2) into (1):

$\begin{gathered} x+\frac{1}{2}x+54=180 \\ \frac{3}{2}x=180-54 \\ \frac{3}{2}x=126 \\ x=\frac{2}{3}\cdot126 \\ x=84 \end{gathered}$

Replace x into (2):

$\begin{gathered} y=\frac{1}{2}(84)+54 \\ y=42+54 \\ y=96 \end{gathered}$

Answer:

The two angles are 84⁰ and 96⁰