Answers

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

   n-2=10

   n=12

   Number of sides of the polygon =12

   Reply
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

   Reply