# Exterior angles of a convex polygon HELP?

• Sep 2nd 2009, 05:25 AM
f1f2f3
Exterior angles of a convex polygon HELP?
I have a problem here which is:
Find the sum of all n exterior angles of a n-sided convex polygon, where n is any positive integer > 3. Show all the working details and reasons.

I need a solution for the general case. So far I know that it is 360 degrees but I am completely unsure of how to start my proof. I am currently 13 years old, so I do not know very advanced maths. Could you please help me here? Thank you very much!
• Sep 2nd 2009, 05:40 AM
Hello f1f2f3
Quote:

Originally Posted by f1f2f3
I have a problem here which is:
Find the sum of all n exterior angles of a n-sided convex polygon, where n is any positive integer > 3. Show all the working details and reasons.

I need a solution for the general case. So far I know that it is 360 degrees but I am completely unsure of how to start my proof. I am currently 13 years old, so I do not know very advanced maths. Could you please help me here? Thank you very much!

Imagine yourself outside a building whose plan view is an n-sided convex polygon. You're standing by one of the walls, facing along the wall. You then walk forward to the first corner of the building - one of the vertices of the polygon. Then you turn to face along the second wall. So you've just turned through an angle equal to the first exterior angle of the polygon.

Then you walk alongside this wall, until you reach the next corner of the building. And - guess what! - turn to face along the third wall. You've then just turned through the second exterior angle of the polygon.

... and so on, until you come back to your starting point. What can you say about the sum of the angles that you've turned through?

Now I realise this isn't a conventional geometry proof, but you can perhaps see how to turn it into one. Have a go!