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Mathematics Question on Sum of the Measures of the Exterior Angles of a Polygon

Find the measure of each exterior angle of a regular polygon of

  1. 9 sides
  2. 15 sides
Answer

(i) Sum of all exterior angles of the given polygon = 360∘360\degree
Each exterior angle of a regular polygon has the same measure.
Thus, measure of each exterior angle of a regular polygon of 99 sides
= 360∘9=40∘\frac{360\degree}{9} = 40\degree

(ii) Sum of all exterior angles of the given polygon = 360∘360 \degree
Each exterior angle of a regular polygon has the same measure.
Thus, measure of each exterior angle of a regular polygon of 1515 sides
=360∘15=24∘\frac{360\degree}{15}=24\degree