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

Explanatory Answer

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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