Are you feeling daunted by the quant section of the GRE? Specifically, question 13 of the second Quantitative section of Practice Test 1 got you puzzled? Don't worry! PrepScholar is here to assist you with your GRE prep, especially when it comes to dealing with polygons.
Survey the Question
To tackle these challenging polygon questions effectively, let's examine the problem for essential clues. Pay close attention to any math-specific terms and specific number patterns. Jot down any noteworthy information that could guide you towards the type of math knowledge required to solve the question.
What Do We Know?
Before diving into problem-solving, let's carefully analyze and list the information we have at hand:
- We are dealing with a regular 9-sided polygon.
- We need to determine the value of an external angle shown in the figure.
Develop a Plan
Now that we have identified what we know, we can devise a step-by-step plan to solve the question. By recognizing that the sum of angles on one side of a straight line is 180°, we can deduce that finding the value of an interior angle will enable us to calculate the external angle.
To find the interior angle of any polygon, we can divide it into triangles. Each triangle has internal angles that sum up to 180°. By multiplying the number of triangles by 180° and dividing by the number of vertices of the polygon, we can determine the value of its interior angle. Drawing triangles on the figure will make the process more straightforward.
Solve the Question
To apply our plan, let's start by drawing triangles from one vertex on the figure, as shown:
By observing the figure, we can see that the sum of all internal angles in our polygon can be represented by seven triangles. To calculate the value of an internal angle within this polygon, we multiply the number of triangles by 180° and then divide by the number of internal angles (which is nine).
Interior Angle of a Polygon = (180° Number of Triangles) / Number of Vertices Interior Angle of a Polygon = (180° 7) / 9 Interior Angle of a Polygon = (9 20° 7) / 9 Interior Angle of a Polygon = 20° * 7 Interior Angle of a Polygon = 140°
We've successfully determined that the interior angle of a 9-sided polygon is 140°. Since the external angle and one interior angle lie on the same side of a straight line, their sum must equal 180°. Therefore, x = 180° - 140°, which means x equals 40°.
Hence, the correct answer is 40°.
What Did We Learn?
Now we understand exactly how to find the interior angle for any regular polygon. By dividing the polygon into triangles, multiplying the number of triangles by 180°, and dividing this sum by the number of vertices (which is also equal to the number of sides of the polygon), we can calculate the interior angle accurately.
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