Calculating Number of Sides in an n-gon with an Average Angle of 175°

[blahblah]

The interior angles of an n-gon have an average measure of 175 degrees. Calculate n.

 

[Jameson]

Hi blahblah,

Welcome to MHB!

If you have a polygon with $n$ sides then each angle can be expressed as \(\displaystyle \frac{(n-2) \times 180^\circ}{n}\). Can you use this formula and the given information to solve for $n$?

Jameson

 

[CaptainBlack]

Hi blahblah,

Welcome to MHB!

If you have a polygon with $n$ sides then each angle can be expressed as \(\displaystyle \frac{(n-2) \times 180^\circ}{n}\). Can you use this formula and the given information to solve for $n$?

Jameson

The implication of the question is that the polygon is not necessarily regular (possibly not even convex) - though given the nature of the question the average of the interior angles of an n-gon is probably an invariant.

In fact it is trivial to show that your formula is the average interior angle for an arbitrary convex n-gon, so that is all-right then!

CB

 

[Jameson]

The implication of the question is that the polygon is not necessarily regular (possibly not even convex)

CB

I don't see that but trust that you know this better than I do. From the level of the other thread the OP made here it seems more likely to me that this is a straightforward question, but I should consider irregular polygons in the future.

EDIT: Ah I think I see your point now. The word "average" could definite imply that the polygon isn't regular although I think it might just be badly worded.

 

[MarkFL]

I have often seen the word n-gon used to describe a regular polygon or isogon, i.e., a polygon with all sides and all angles equal.

However, when I saw the term "average measure" for the interior angles, I assumed then a convex polygon, not necessarily regular, as the same number of sides results either way.