GMAT Sample Question - Geometry
March 19, 2004
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 |
Correct choice (A) Correct answer (10 sides)
Solution:
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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