if each exterior angle on a regular polygon has a measure of 12 degrees, how many sides will the polygon have?

Question

calculate the value of x in the polygon.

 

In the polygon at the top it is x+14 degrees

to the left of that is x

and to the right of that is an arrow saying 83 degrees

Answer 1

The sum exterior angels of all regular polygons is 360°

360 / 12 = 30

Answer 2

Hi Michelle,

 

I am assuming this is is a regular polygon. Please confirm that!

 

If the measure of exterior angle is 12, then the interior angle will be 180-12 = 168 deg

 

the measure of an interior angle in a polygon with n sides is equal to

 

180*(n-2) / n

 

so we can write

168 = 180*(n-2) / n

168n = 180n - 360

n = 30 This polygon will have 30 sides if it is regular.

 

The rest of your question is impossible to solve without a figure.