How ’bout them stars?
First off, I must address the title. If I hear the words “How about them Sox?” one more time, I will enter into a state of irrevoverable insanity. That said, how about them stars?
Ah, yes, those stars…Let ABCDE Be a regular pentagon. Drawing a line contecting angle x to the next non-adjacent angle going around until the original angle is reached will form a 5 pointed star. What is the degree measure of the point of the star? There are numberous ways to go about solving this, but I will go with what I believe to be the more direct algebraic way. It may be noted that when Drawing line AC, or any such line, an Isoseles Triangle is formed. Drawing two of these “star lines” in a row will for the point of the star. The point of the star is the original angle measure of the regluar polygon, minus 2 times the base measure of the isoseles triangle (they are conguent)…I will try to get some pictures of that formula up…The base angles of the isoseles triangles are the quantity 180 minus an original angle divided by two. in the pentagon, this is 36…then 108 - 2(36) is also 36. yay! i don’t know why I post on weird things like this…