![]() Polygons must have at least three sides as a two-sided shape cannot be closed. When sides do not cross each other, we call them "simple polygons." For this article, we will only be using simple polygons. It comes from the Latin poly meaning "many" and gōnia, meaning "angle." "Closed," in this context, means that the sides form a complete circuit. This definition does not exclude shapes such as an hourglass or a star where sides cross each other. Have questions? Leave a comment or send us an email at. Want more expert GRE prep? Sign up for the five-day free trial of our PrepScholar GRE Online Prep Program to access your personalized study plan with 90 interactive lessons and over 1600 GRE questions. We can just divide it into triangles, get the total sum of the interior angles of the polygon by multiplying the number of triangles by $180°$, then dividing this sum by the number of vertices of the polygon (which is also equal to the number of sides of the polygon). Now we know exactly how to find the interior angle for any regular polygon. We can see that $x$ and one interior angle lie on the same side of a straight line, so their sum must be $180°$. $$Įxcellent! So the interior angle of a $9$-sided polygon is $140°$. To find the value of an internal angle within this polygon, we can just multiply the number of triangles by $180°$, then divide by the number of internal angles, which is nine. So here we can see that the sum of all of the internal angles in our polygon can be represented as seven triangles. ![]() This won’t be as difficult as it sounds, particularly once we start drawing the triangles on our figure.įirst, let’s draw triangles starting at one vertex in our figure, like this: Then multiply the number of triangles by $180°$ and finally divide by the number of vertices of the polygon to get the value of its interior angle. To find the interior angle of any polygon, we can divide it into triangles, knowing that all triangles have internal angles that sum up to $180°$. We know that the sum of angles on one side of a straight line is $180°$ from the figure, we can see that if we can find the value of the interior angle at one vertex of the polygon, then we can subtract that value from $180°$ to get the value of $x$. We want to know the value of an external angle to that polygon shown in the figure. ![]() Let’s carefully read through the question and make a list of the things that we know. Let’s keep what we’ve learned about this skill at the tip of our minds as we approach this question. Pay attention to any words that sound math-specific and anything special about what the numbers look like, and mark them on our paper. Let’s search the problem for clues as to what it will be testing, as this will help shift our minds to think about what type of math knowledge we’ll use to solve this question. Those questions testing our knowledge of Polygons can be kind of tricky, but never fear, PrepScholar has got your back! Survey the Question Buuuut then you had some questions about the quant section-specifically question 13 of the second Quantitative section of Practice Test 1. So, you were trying to be a good test taker and practice for the GRE with PowerPrep online. The figure above shows a regular 9-sided polygon. ![]()
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