In a certain regular polygon, the measure of each interior angle is 12 times the measure of each exterior angle. Find the number of sides in this regular polygon.
If I knew the value of an angle I could work backwards from (n – 2) • 180.
To obtain the value of an angle, I'm going to have to divide 180 by 13.
That division doesn't come out even, so I'm stuck there. Sorry.
The answer is 36 sides.
Let's try it out.
Using (n – 2) x 180o we find the sum of all 36 angles = 6,120o
Since it's a regular polygon each of the 36 angles must equal 6,120o / 30 = 170o
This leaves only 10o for the external angle. That doesn't have the required 12 to 1 ratio.
Have I made a mistake somewhere? What say you?