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Geometry - March 19, 2004

The GMAT Sample Math question for the day is from the topic Geometry.

Question
If the sum of the interior angles of a regular polygon measures up to 1440 degrees, how many sides does the polygon have?

A. 10 sides
B. 8 sides
C. 12 sides
D. 9 sides
E. None of these

The correct choice is (A) and the correct answer is 10 sides.

Explanatory Answer
We know that the sum of an exterior angle and an interior angle of a polygon = 1800.

We also know that sum of all the exterior angles of a polygon = 3600.

The question states that the sum of all interior angles of the given polygon = 14400.

Therefore, sum of all the interior and exterior angles of the polygon = 1440 + 360 = 1800

If there are ‘n’ sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800

Therefore, n = 10.
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