1. The problem asks for the sum of the interior angle measures of a convex 18-gon, which is a polygon with 18 sides. 2. The formula to find the sum of interior angles of a polygon with $n$ sides is: $$\text{Sum of interior angles} = (n - 2) \times 180^\circ$$ 3. Here, $n = 18$. 4. Substitute $n = 18$ into the formula: $$\text{Sum} = (18 - 2) \times 180^\circ$$ 5. Simplify inside the parentheses: $$\text{Sum} = 16 \times 180^\circ$$ 6. Multiply: $$\text{Sum} = 2880^\circ$$ 7. Therefore, the sum of the interior angle measures of a convex 18-gon is $2880^\circ$.