Quandaries
and Queries 

The measure of each interior angle of a regular polygon is eight times that of an exterior angle of the polygon. How many sides does the polygon have?
Thanks for your help! 

Hi Melissa, I'm not very good at remembering formulas. I would do this with a diagram. PQ and QR are two adjacent sides of the polygon, C is the center of the polygon and e is an external angle. If there are n sides to the polygon then the angle RCQ (the angle s) is 360/n degrees. The angles labeled t are all equal and you know that 2t = 8e. 2t + e = 180 degrees and 2t + s = 180 degrees and hence s = e.Hence
and thus n = 18. Cheers, 

