Question

The exterior angle of a regular polygon is one-sixth of its interior angle. How many sides does the polygon have?

Answer 1

Answer:

Step-by-step explanation:

A closed plane shape bounded by three or more line segments is called a polygon.

Some polygons have names based on the number of sides. Otherwise, a polygon with n sides is called n-gon. For example a polygon that has 15 sides is called 15-gon.

When all the sides of a polygon are equal in length and all its angles are equal in magnitude, it is called a regular polygon.

E.g →  An equilateral triangle and a square are regular polygons.

 

An Interior angle of a regular polygon  

An Interior angle of a regular polygon=  

 

Step 1 of 2

Write the given information :

The exterior angle of a regular polygon is one-fifth of its interior angle.

Let the interior angle be x and exterior angle will be (180° - x ).

Answer 2

Answer:

hope it helps you

Step-by-step explanation:

Sum of exterior and interior angles is 180 deg.

If the interior angle is 3x, the exterior angle is x. Hence 3x+x = 4x = 180 or x = 45. The interior angle is 135 deg. So the polygon has 360/45 = 8 sides or it is a regular octagon.