A polygon has each exterior angle equal to 30 degrees. How many sides does it have ?

### 1 Answer | Add Yours

We use the property that the sum of all the angles of a polygon with n sides is equal to 180*(n - 2).

If the exterior angles are equal to 30 degrees, the interior angles are equal to 180 - 30 = 150 degrees.

If there are n-sides in the polygon, the sum of all n angles would be equal to 150*n

Equating 150*n = 180*(n - 2)

=> 150n = 180n - 360

=> 30n = 360

=> n = 360/30

=> n = 12

**The polygon has 12 sides.**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes