SOLUTION: prove that the sum of the angles of any quadrilateral is 360 degrees. does it have to do with the expression: (n-2)180 where n is the number of sides?

Question 147340: prove that the sum of the angles of any quadrilateral is 360 degrees.
does it have to do with the expression: (n-2)180
where n is the number of sides?
Answer by nabla(475) (Show Source): You can put this solution on YOUR website!
Yes, you can form a corollary from the rule (n-2)180.
Case n=4 then 2*180=360.
However, a more exhaustive proof is better.
Conjecture (Quadrilateral Sum ): The sum of the measures of the interior angles in any convex quadrilateral is 360 degrees.
Proof: We can break a convex quadrilateral into 2 triangles. Because the angles in a triangle add to 180 degrees by a Triangle Sum Conjecture, we have 2*180=360.
QED
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