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Geometry. - Quant/Math - CAT 2009
Question 4 the day:
March 19, 2004
The question for the day is about polygons and the number of sides of a polygon from the topic geometry
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If the sum of the interior angles of a regular polygon measures up to 1440 degrees, how many sides does the polygon have?
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10 sides
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(2) |
8 sides
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| (3) |
12 sides
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(4) |
9 sides
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Correct choice - (1)
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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