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=(1)/(2)x+54_{\text{ }}(2)`

Replace (2) into (1):

`\begin{gathered} x+(1)/(2)x+54=180 \\ (3)/(2)x=180-54 \\ (3)/(2)x=126 \\ x=(2)/(3)\cdot126 \\ x=84 \end{gathered}`

Replace x into (2):

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

Answer:

The two angles are 84⁰ and 96⁰