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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?

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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1 Answers

vijay narang
27 Points
13 years ago

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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