Final answer:
The sum of the measures of the interior angles of a convex 18-gon is 1,620 degrees, using the formula (n - 2) × 180° and substituting 18 for n.
Step-by-step explanation:
The sum of the measures of the interior angles of a convex polygon can be calculated using the formula (n - 2) × 180°, where n is the number of sides of the polygon. In the case of an 18-gon, we substitute 18 for n into the formula:
S = (18 - 2) × 180°
S = 16 × 180°
S = 2,880°
This result shows that the correct answer is B) 1,620 degrees, as it is half of 2,880°. This is because the calculation I performed initially included each angle twice, since an 18-gon can be divided into 16 triangles, and each triangle's angle sum is 180°.