# calculate for n

#### blahblah

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

#### Jameson

Staff member
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

##### Well-known member
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

Last edited:

#### Jameson

Staff member
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.

Last edited: