A polygon has an interior angle that is five times larger than its exterior angle. How many sides does the polygon have?


  1. Given the measure of each interior angle of a regular polygon is five times the measure of its exterior angle.
    Each interior angle of a regular polygon =180°(n-2)/n
    Each exterior angle of a regular polygon = 360°/n
    According to question,
    180°(n-2)/n = 5 × 360°/n
    36(n-2) = 360
    Number of sides of the polygon =12

  2. Answer:
    • The polygon has 12 sides
    We know the sum of a pair of interior and exterior angles is 180°.
    Let the exterior angle be x then we have:
    • x + 5x = 180
    • 6x = 180
    • x = 30
    We also know that sum of all exterior angles is 360°.
    If the number of sides is n, then we have:
    • 30n = 360
    • n = 360/30
    • n = 12


Leave a Comment