Question

If an exterior Angele of a regular polygon is an integer, what are the possible values of the angle?​

Answer 1

Please read the explanied answer below.

Explanation:

• As we know that polygon is a shape that consists of at least three sides.

• The sum of exterior angles of any polygon =
  `360^(\circ )`

We also know that a regular polygon has all the angles equal and all sides have the same length.

As we know:

• Exterior angle = 360° ÷ No. of sides

When the number of sides changes, the angle also changes. Therefore, we would get different integers as answer.

For example:

In terms of a triangle:

Exterior angle = 360° ÷ No. of sides

= 360° ÷ 3 = 120°

In terms of a rectangle:

Exterior angle = 360° ÷ No. of sides

= 360° ÷ 4 = 90°

and in the same way

360° ÷ 5 = 72 °

360° ÷ 6 = 60 °

360° ÷ 8 = 45 °

360° ÷ 9 = 40°

and so on.

I hope it may have solved your query.