Question

The sum of the measures of the exterior angles of a regular 9-gon, one at each vertex, is ____ the sum of the measures of the exterior angles of a regular 6-gon, one at each vertex.

Answer 1

9-gon one ext. angle is 40 degrees, all are 360, 6-gon one ext. angle is 60 degrees, total is 360.

Answer 2

Answer: The sum of the measures of the exterior angles of a regular 9-gon, one at each vertex, is equal to the sum of the measures of the exterior angles of a regular 6-gon, one at each vertex.

Explanation:

We know that If we count one exterior angle at each vertex of all regular polygon, then the sum of the measures of the exterior angles of a polygon is always
`360^(\circ)`.

Thus, the sum of exterior angle is same for regular 9-gon and regular 6-gon.

Therefore, the sum of the measures of the exterior angles of a regular 9-gon, one at each vertex, is equal to the sum of the measures of the exterior angles of a regular 6-gon, one at each vertex.