This GMAT quant practice question is a problem solving question in Geometry. Concept: Interior angles of polygons

Question 4: If the sum of the interior angles of a regular polygon measures 1440°, how many sides does the polygon have?

- 10 sides
- 8 sides
- 12 sides
- 9 sides
- None of these

@ INR

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

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

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

Therefore, sum of all the interior and all 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.**

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

So, (n - 2) × 180 = 1440

Or n - 2 = 8

=> **n = 10**

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