# GMAT Practice Question - Geometry Polygons

Concept: Comparison of 2 powers in different intervals

This GMAT quant practice question is a problem solving question from Geometry. Concept: Polygons and interior angles in geometry.

#### Question: If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have?

1. 10 sides
2. 8 sides
3. 12 sides
4. 9 sides
5. None of these

Video explanation will be added soon

#### Compute sum of all interior and exterior angles

The sum of an exterior angle and an interior angle of a polygon = 180o.

The sum of all the exterior angles of a polygon = 360o.

From the question stem: sum of all interior angles of the given polygon = 1440o.

Therefore, sum of all the interior and all exterior angles of the polygon = 1440 + 360 = 1800o.

#### Compute number of sides

If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n = 1800o.

Therefore, n = 10.

Choice A is the correct answer.

#### Alternative Approach : Using formula

Sum of all interior angles of a convex polygon = (n - 2)* 180

So, (n - 2) * 180 = 1440

n - 2 = 8

n = 10

Choice A is the correct answer.

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