Final answer:
The sum of the measures of the interior angles of a convex polygon with 5 vertices is calculated using the formula (n - 2) × 180°, which gives us 540°.
Step-by-step explanation:
To determine the sum of the measures of the interior angles of a convex polygon with 5 vertices, you can use the formula for finding the sum of the interior angles of a polygon, which is (n - 2) × 180°, where n is the number of sides or vertices of the polygon. For a polygon with 5 vertices:
Sum of interior angles = (5 - 2) × 180°
Sum of interior angles = 3 × 180°
Sum of interior angles = 540°
Therefore, the correct answer is C. 540°. This result is derived from the general formula for the sum of interior angles in a convex polygon, where each interior angle is the angle formed by two adjacent sides inside the polygon. In this polygon with 5 vertices, the sum of these angles is 540°.