In a convex heptagon, the degree measures of the interior angles are $x, ~x, ~x-2, ~x-2,
~x + 2, ~x + 2$ and $x + 4$ degrees. What is the degree measure of the largest interior angle?
A heptagon is a polygon with seven sides, so the sum of the interior angles of a convex heptagon is $(7-2) \times 180 = 900$ degrees. I can write an equation using this fact and the given angle measures: $x + x + (x-2) + (x-2) + (x+2) + (x+2) + (x+4) = 900$. Simplifying this equation, I get $7x + 4 = 900$, so $7x = 896$ and $x = 128$. The largest interior angle is $x + 4 = 132$ degrees. 