Geometric Questions Answers

Quant/Math - CAT 2008

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

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

(1)	10 sides			(2)	8 sides
(3)	12 sides			(4)	9 sides

Correct choice - (1)

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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.