Question

Find the measure of each exterior angle of a regular polygon of 15 sides

Answer 1

Answer:

Measure of each of the  exterior angles of 15 sided regular polygon is = 24°

Step-by-step explanation:

From one vertex of n sided polygon, we can draw (n-3) diagonals.  This is because the two adjacent vertices form adjacent sides and not diagonals.  So, from the n number of vertices, one is the vertex itself from where we are drawing the diagonals, and we have just discussed about the two adjacent vertices.

With n - 3 diagonals from one vertex, we will get (n - 2) triangles dividing all the interior angles of the n sided polygon amongst themselves.  

Therefore, the sum of the interior angles of n sided regular polygon is (n - 2)x180°

Therefore, the sum of the interior angles of 15 sided regular polygon is (15 - 2)x180°  = 13x180°

Therefore, each of the  interior angles of 15 sided regular polygon is = 13x180°/15

Therefore, each of the  exterior angles of 15 sided regular polygon is = 180° - 13x180°/15 = 180°(1 - 13/15) = 180°x2/15 = 12°x2 = 24°

Answer 2

Step-by-step explanation:

The sum of the exterior angles of a regular polygon is 360°

Number of sides of polygon =15

As each of the exterior angles are equal,

Exterior angle = 360/15° =24°

Hope this is helpful for you.