Impasta

You're supposed to express the exponent of x in terms of n and k.

Actually, the Pascal's Triangle bit is a bit misleading... the Binomial Theorem is your best friend here.

I REALLY suggest you look back and see what the other guy said about the sum of the interior angles of a polygon. You can do this problem by yourself and you shouldn't even need help.

But hey, cheer up! I used to be in the same boat as you, thinking I was never going to get good at geometry. But as I did more problems and did more practice, I can say that I am thinking slightly less that I am never going to get good at geometry. Woohoo.

I'm fairly certain there's no way that can be the answer. Sorry. And anyway, Pascal's Triangle is really interesting and you should check it out. There are countless things you can do with it. In this case, Pascal's Triangle's numbers are also combinations, which is really cool. This means you can use it as a way to find the coefficients in the Binomial Theorem, although 9 times out of 10 you're better off just computing the combination.

A little vague, so ask me if you need clarification.

Geometry questions are always a nightmare to write answers to, but I'll give it my best shot. If we connect CH, we get a right triangle. The interior angle of a regular octagon is 135 degrees (make sure you see why!). Therefore, with CH being perpendicular to GH, we know that angle AHC= 45 degrees. Therefore, angle P is I believe 45 degrees. 

Very nice! See, I knew you could do it by yourself :)