Explanation
a linear pair of angles must add up to 180 degrees,
Step 1
Let
x= angle1
y= angle2
then
[tex]x+y=180\text{ Equation(1)}[/tex]Also
One angle is a fifth the size of the other angle, then
[tex]x=\frac{y}{5}\text{ Equation (2)}[/tex]Step 2
replace the value of x from equation(1) in equation(2)
[tex]\begin{gathered} x=\frac{y}{5} \\ so, \\ \frac{y}{5}+y=180 \\ \frac{6}{5}y=180 \\ y=\frac{180\cdot5}{6} \\ y=150 \end{gathered}[/tex]Step 3
replace the value of y=150 in equation (2) to find x
[tex]\begin{gathered} x=\frac{y}{5} \\ x=\frac{150}{5} \\ x=30 \end{gathered}[/tex]Hence, the answer is 30 and 150
