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.

Guest May 10, 2020

#1**0 **

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.

Guest May 10, 2020

#2

#3**0 **

Let's try it out.

Using (n – 2) x 180^{o} we find the sum of all 36 angles = 6,120^{o}

Since it's a regular polygon each of the 36 angles must equal 6,120^{o} / 30 = 170^{o}

This leaves only 10^{o} for the external angle. That doesn't have the required 12 to 1 ratio.

Have I made a mistake somewhere? What say you?

_{.}

Guest May 12, 2020