36 and 144
Explanation
Two Angles are Supplementary when they add up to 180 degrees
Step 1
Let
x= angle 1
y= angle2
The measure of one angle is four times the measure of the other angle,then
[tex]\begin{gathered} \text{angle}1=4\cdot\text{angle}2\text{ } \\ x=4y\text{ Equation(1)} \end{gathered}[/tex]x and y are supplementary angles , then
[tex]x+y=180\text{ Equation (2)}[/tex]Step 2
use Equation (1) and (2) to find x and y
[tex]\begin{gathered} x=4y \\ x+y=180 \end{gathered}[/tex]replace Equation (1) in Equation (2)
[tex]\begin{gathered} 4y+y=180 \\ 5y=180 \\ y=\frac{180}{5} \\ y=36 \end{gathered}[/tex]replace the value of y= 36 in equation (1) to find x
[tex]\begin{gathered} x=4y \\ x=4\cdot36 \\ x=144 \end{gathered}[/tex]Hence, the answer is 36 and 144
