Problem 6

1. Problem 6 By: Jeremy Duggan

2.

4. �Let�s try to derive a formula for the sum of the interior angles for a convex polygon with any number of sides.� �First let�s make a polygon with �n� number of sides and �n� number of angles.� Draw the polygon and label the angles. �Then pick an angle.� Highlight angle 4 �From that angle, draw a line connecting it to every non-adjacent angle, which will create (n-2) triangles.� Draw lines connecting angle 1 to all the other non-adjacent angles. �Remember that a triangle�s interior angles have a sum of 180 degrees.� �Add up the interior angles of the triangles that were created when angle 4 was connected to every non-adjacent angle.� Put 180� into each triangle. Add the 180� from each triangle together. �You will then have to add 180� to itself �n-2� times. �We can then rewrite the formula as (n-2)180 Draw =(n-2)(180).�Let�s try to derive a formula for the sum of the interior angles for a convex polygon with any number of sides.� �First let�s make a polygon with �n� number of sides and �n� number of angles.� Draw the polygon and label the angles. �Then pick an angle.� Highlight angle 4 �From that angle, draw a line connecting it to every non-adjacent angle, which will create (n-2) triangles.� Draw lines connecting angle 1 to all the other non-adjacent angles. �Remember that a triangle�s interior angles have a sum of 180 degrees.� �Add up the interior angles of the triangles that were created when angle 4 was connected to every non-adjacent angle.� Put 180� into each triangle. Add the 180� from each triangle together. �You will then have to add 180� to itself �n-2� times. �We can then rewrite the formula as (n-2)180 Draw =(n-2)(180).