Final answer:
The equation (n - 2) × 180° = 6120° helps to determine that a polygon with a sum of its interior angles equal to 6120° has 36 sides.
Step-by-step explanation:
The student's question appears to be related to the formula for finding the sum of the interior angles of a polygon. The formula is given as (n - 2) × 180°, where n represents the number of sides of the polygon. When the sum of the interior angles is given as 6120°, as per the question, we can set up an equation to solve for n.
Beginning with the formula:
We then divide both sides by 180° to isolate (n - 2) and solve for n:
- n - 2 = 6120° / 180°
- n - 2 = 34
- n = 34 + 2
- n = 36
Therefore, a polygon with a sum of its interior angles equal to 6120° has 36 sides.