# Geometry : Properties of Polygons

This quant practice question is a problem solving question in geometry. Concept Tested: Properties of polygons; number of sides of a regular polygon and sum of its interior angles and exterior angles.

## Question

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 Answer      Choice (1). The polygon has 10 sides.

## Explanatory Answer

We know that the sum of an exterior angle and the corresponding interior angle of a polygon = 180o.
We also know that sum of all the exterior angles of a convex polygon = 360o.

The question states that the sum of all interior angles of the given polygon = 1440o.
Therefore, sum of all the interior and exterior angles of the polygon = 1440 + 360 = 1800o ..... (1)
If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 * n ..... (2)
Equate information in (1) and (2): 180n = 1800
Therefore, the number of sides in the polygon, n = 10.

The correct answer is Choice (1).

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