What is the sum of the interior angles of a quadrilateral?

Answer 1

The interior angles of a quadrilateral (polygon with 4 sides and angles) sum to 360 degrees. We can find this in a couple of ways. First, noting the general formula for an n-gon:

S = (n - 2)(180)

where S is the sum of the interior angles in degrees and n is the number of sides of the n-gon. We find S = (4 - 2)(180) = 360 degrees.

Second, the exterior angles must average 360/n degrees. In this case, 360/4 = 90 degrees. Interior angles are supplementary to exterior angles, so the average interior angle must equal 90 degrees. Finally, 4 interior angles with an average of 90 degrees means a sum of 360 degrees.

Finally, consider some quadrilaterals (e.g. squares, rectangles, parallelograms, etc.). They each contain 360 degrees (e.g. four 90 degree angles).

Answer 2

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