Expert: Cynthia Watanabe - 5/15/2006

Question
hi, i am in the 12th grade. i wanted to know what is the sum of the interior angles of a convex quadrilateral. i know its either 180 or 360 degrees but dont know which exactly. thanks alot!

Answer
Hannah,

A convex quadrilateral can look like a rectangle but doesn't have to have 4 right angles.

Now there's a formula for finding the sum of the interior angles of a polygon.  The formula is (n-2)*180 degrees.  n stands for the number of sides of the polygon.

Since a quadrilateral has 4 sides, substitute 4 into the formula. So the sum of the angles of a quadrilateral is (4-2)*180 degrees.  Do the arithmetic and you have your answer!

Here's a webpage that explains the formula and gives examples:
http://regentsprep.org/Regents/math/poly/LPoly1.htm
or
http://regentsprep.org/Regents/math/poly/JavaIntAngles.htm

Keep asking questions! Take care, Cynthia