Is there a relationship between degrees of angles in a polygon to it's diagonals?

You're referring to what JeffM said in post #10, right?

I have no idea what he meant.
What I meant was 1:1. Diagonals AC, AD, BD, BE, CaA, CE. Each of the five vertices has 2 non-neighboring vertices so 2 distinct diagonals can be defined with respect to any vertex. But AC and CA are the same diagonal. So there are 5 distinct diagonals and 5 interior angles. That defines a ratio of 1:1 between the number of angles and the number of diagonals in a pentagon. (This is not a general result for polygons. A square has 2 diagonals, but 4 interior angles. A hexagon has 3 or 9 diagonals, depending on how we define diagonal, but 6 interior angles.)

I shall correct my original post. Failed to proof carefully. Apologies to all.
 
Are you asking about a relationship between the measure of each interior angle of a regular polygon, and the number of diagonals of that polygon? Or something else, like the sum of the measures of the angles, and something about the lengths of diagonals or angles between them?

If it's the former, then each quantity is related to the number of vertices, so there is an indirect relationship between them. Do you know these two relationships?
What are the two relationships?
[I don't understand the underlined text? Can you help me?...]
 
What are the two relationships?
[I don't understand the underlined text? Can you help me?...]

I'd like you to tell me whether you are familiar with these, because I would expect you to have seen at least one of them before asking the sort of questions you have had.

First, how many diagonals are there in an n-gon (a polygon with n sides)? This does not depend on it being regular (though, depending on your definition of a diagonal, you may require it to be convex).

Second, what is the measure of each interior angle of a regular n-gon? Or, for any polygon, what is the sum (or average) of the angles?

Each of these is well-known, and if you haven't been taught them, you can find them easily by searching the internet. I did ...
 
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