What are the measures of an interior angle and a exterior angle of a regular 30-gon?

Question

I need help with this question because the measures im getting are to high to fit the polygon measure. Please help!

Answer 1

Any polygon's exterior angles add up to 360º.

 

Picture a Pentagon:  (see the image at the URL below)  The exterior angles basically go around the polygon, filling in a circle until it is full (360º)

 

http://www.mathsisfun.com/geometry/images/exterior-angles-polygon.gif

 

Also, the interior angles of any polygon add up to however many triangles we can make out of that polygon * 180º per triangle.  Picture a square.  You can make two triangles out of that, so the interior angles add up to 180º * 2 = 360º.

 

Picture a pentagon 5 sides.  You can make three triangles out of that shape, so the interior angles add up to 180º * 3 = 540º

 

Picture a hexagon 6 sides.  You can make four triangles out of that shape, so the interior angles add up to 180º * 4 = 720º.  

 

Do you see a pattern emerging?  The equation for the interior angles of any sided polygon of number of sides s is : (s - 2) * 180

 

So, for your 30-gon, the interior angles total up to (30-2) * 180 = 5040.   Each interior angle is that total divided by the number of interior angles, or 5040/30 = 168º:

 

The measure of each exterior angle is the total divided by the number of angles, or 360/30 = 12º.