Demystifying GRE Math: Mastering Polygons and Angles

CEO Khai Intela
Are you preparing for the GRE and feeling a little stuck on the quant section? Don't worry - we've got your back! In this article, we'll break down a tricky question about polygons and angles...

Are you preparing for the GRE and feeling a little stuck on the quant section? Don't worry - we've got your back! In this article, we'll break down a tricky question about polygons and angles to help you gain a deeper understanding of this topic. So, let's dive in and conquer those math problems together!

Surveying the Question

Before we jump into finding a solution, let's take a moment to analyze the problem. Understanding what the question is testing will guide us in applying the right math knowledge to solve it. Look for math-specific terms and any special characteristics of the given numbers. Mark down these details on your paper to keep them fresh in your mind.

What Do We Know?

Now that we have surveyed the question, let's carefully read through it and make a list of the information we already know. In this case, we are dealing with a regular 9-sided polygon and we need to find the value of an external angle shown in the figure.

Developing a Plan

To solve this question, we need to find the interior angle of the polygon and then subtract that from 180° to get the value of the external angle. Fortunately, we can use a simple approach to find the interior angle of any polygon. By dividing the polygon into triangles, we can take advantage of the fact that the sum of angles in any triangle is 180°. Let's start drawing triangles on our figure to make this process easier.

Solving the Question

After drawing triangles starting from one vertex of our polygon, we can see that the sum of all the internal angles can be represented by seven triangles. To find the value of the interior angle, we can multiply the number of triangles by 180° and then divide by the number of vertices (which is 9 in this case).

So, the interior angle of the polygon is (180° * 7) / 9, which simplifies to 140°. Now, since the external angle and one interior angle lie on the same side of a straight line, their sum must be 180°. Therefore, the value of the external angle (x) is 180° - 140°, which equals 40°.

The correct answer is 40°!

What Have We Learned?

By tackling this question, we have gained a solid understanding of how to find the interior angle of any regular polygon. You can simply divide the polygon into triangles, calculate the sum of the interior angles by multiplying the number of triangles by 180°, and then divide this sum by the number of vertices (which is also equal to the number of sides).

Now that you have mastered polygons and angles, you're one step closer to acing the GRE math section. Keep practicing and honing your skills, and you'll be well-prepared for any math question that comes your way.

Remember, if you want expert GRE prep tailored to your needs, sign up for our five-day free trial of the PrepScholar GRE Online Prep Program. Access personalized study plans, interactive lessons, and over 1600 GRE questions to take your preparation to the next level.

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