Angles $A$ and $B$ are supplementary. If the measure of angle $A$ is $8$ times angle $B$, what is the measure of angle A?
I know that supplementary angles add up to $180$ degrees, so I can write an equation using that fact: $A + B = 180$. I also know that $A$ is $8$ times $B$, so I can write another equation using that fact: $A = 8B$. Now I have a system of two equations with two unknowns, and I can use substitution to solve it. I can substitute $8B$ for $A$ in the first equation, and get $8B + B = 180$. Simplifying, I get $9B = 180$, so $B = 20$. Then, to find $A$, I can plug in $B = 20$ into the second equation, and get $A = 8(20)$. Simplifying, I get $A = 160$. So the measure of angle $A$ is $160$ degrees. 