GMAT Quant Questions | Geometry #4

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?

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

---

---

Video Explanation

---

---

Explanatory Answer | GMAT Geometry

Step 1 of answering this Geometry question: Compute sum of all interior and exterior angles

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°.

Step 2 of answering this Geometry question: Compute number of sides

If there are 'n' sides to this polygon, then the sum of all the exterior and interior angles = 180 × n = 1800°.
Therefore, n = 10.

Choice A is the correct answer.

---

Alternative Approach: Using the formula

Sum of all interior angles of a convex polygon = (n - 2) × 180
So, (n - 2) × 180 = 1440
Or n - 2 = 8
=> n = 10

Choice A is the correct answer.