Understanding a Regular Polygon Problem: Exterior Angle 120° and Side Length 5 (Ages 12+)

Learn how to find the perimeter of a regular polygon using exterior angle and side length: compute number of sides from exterior angle, then multiply by side length.

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Step-by-step solution

We’re given a regular polygon with side length 5 units and an exterior angle of 120°. We want its perimeter.

  1. Relate exterior angle to number of sides: In any regular polygon, the exterior angle equals 360° divided by the number of sides (n):

    Exterior angle = 360°/n

  2. Solve for n: 120° = 360°/n

    Multiply both sides by n: 120n = 360

    Divide by 120: n = 360/120 = 3

    So the polygon is a triangle (3 sides).

  3. Compute the perimeter: Perimeter = (number of sides) × (side length) = n × 5 = 3 × 5 = 15 units.

Answer: The perimeter is 15 units.

Key takeaway for statistics context

In statistics, this type of reasoning shows how a known rate or angle (like an exterior angle) can determine a count (number of sides). Similarly, knowing a unit rate (e.g., length per side) allows you to scale up to a total (perimeter). Understanding how to translate a given measurement into a quantity (n) and then using that to find a total (perimeter) is a common pattern when modeling data or solving geometric-statistical problems.

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