Final answer:
The sixth angle of a convex heptagon with seven consecutive angle measures can be found by using the formula for the sum of the interior angles of a polygon (n-2) × 180°, representing the angles as consecutive values, and solving for the unknown. The closest answer to the calculated value is 131°.
Step-by-step explanation:
To find the measure of the sixth angle in a convex heptagon with seven consecutive angle measures, we'll first need to remember the formula for finding the sum of the interior angles of a polygon: (n-2) × 180°, where n is the number of sides of the polygon.
Since we have a heptagon, which is a 7-sided polygon, the sum of its angles will be (7-2) × 180° = 5 × 180° = 900°. Now, if the angles are consecutive, we can represent them as x, x+1, x+2, x+3, x+4, x+5, and x+6, where x is the measure of the smallest angle.
Adding all these angles together should equal the sum of the interior angles of the heptagon: x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) = 900°. This simplifies to 7x + 21 = 900°. Solving for x gives us x = (900° - 21°)/7 = 879°/7 = 125.57°.
Therefore, the measure of the sixth angle, which is x+5, would be 125.57° + 5 = 130.57°. However, this is not an option listed, so we must consider the possible rounding off. The option closest to our calculated value is (c) 131°.