The GMAT Math practice question is a problem solving question on Polygons and interior angles in geometry
If the sum of the interior angles of a regular polygon measures up to 1440 degrees, how many sides does the polygon have?
- 10 sides
- 8 sides
- 12 sides
- 9 sides
- None of these
The correct choice is (A) and the correct answer is 10 sides
We know that the sum of an exterior angle and an interior angle of a polygon = 180o.
We also know that sum of all the exterior angles of a polygon = 360o.
The question states that the sum of all interior angles of the given polygon = 1440o.
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.