A convex pentagon has interior angles with measures $x+1$, $2x$, $3x$, $4x$, and $5x-1$ degrees.  What is the measure of the largest angle?
I know that the sum of the interior angles of any convex pentagon is $180(5-2) = 540$ degrees, so I can write an equation using that fact and the given angle measures. I have $x+1 + 2x + 3x + 4x + 5x-1 = 540$. Simplifying, I get $15x = 540$, so $x = 36$. The largest angle is the one with the coefficient $5x$, so it has measure $5x-1 = 5(36)-1 = 179$ degrees. 