Prove with induction that all convex polygons with n≥3 sides have interior angles that add up to (n-2)·180 degrees. you may assume that a triangle has interior angles that add up to 180 degrees.

Hence by induction proved for all natural numbers n.

Step-by-step explanation:

we are to Prove with induction that all convex polygons with n≥3 sides have interior angles that add up to (n-2)·180 degrees.

Starting from triangle we can assume that angles of a triangle add up to 180

Imagine one side say AB.  From A and B two lines are drawn to meet at D

Now BADC is a quadrilateral.  The sum of angles of a quadrilateral would be sum of angles of two triangles namely ABC and BDC.  hence these add up to 360.

Thus when we make n from 3 to 4 this is true.

Let us assume for n sides sum of angles is (n-2)180 degrees. Take one side vertices and draw two lines so that the polygon is n+1 sided.  Now the total angles would be the sum of angles of original polygon+angles of new triangle = (n-2)180+1 = (n+1-2)180

Thus if true for n it is true for n+1.  Already true for 3 and 4.

Hence by induction proved for all natural numbers n.