So, you were trying to it is in a an excellent test taker and also practice because that the GRE v PowerPrep online. Buuuut climate you had some questions about the quant section—specifically question 13 that the 2nd Quantitative ar of exercise Test 1. Those questions testing our understanding of Polygons have the right to be sort of tricky, yet never fear, has obtained your back!

Survey the Question

Let’s search the difficulty for clues regarding what it will be testing, together this will certainly help change our minds come think about what kind of math understanding we’ll use to solve this question. Pay attention to any type of words that sound math-specific and also anything special around what the numbers look like, and mark them on our paper.

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Let’s store what we’ve learned about this ability at the reminder of ours minds together we technique this question.

What carry out We Know?

Let’s very closely read through the question and make a perform of the points that we know.

We have actually a continuous $9$-sided polygonWe want to understand the worth of an external angle to that polygon displayed in the figure

Develop a Plan

We understand that the sum of angle on one next of a directly line is $180°$ native the figure, we deserve to see the if us can discover the value of the internal angle in ~ one vertex of the polygon, then we can subtract that worth from $180°$ to acquire the worth of $x$.

To uncover the internal angle of any polygon, we deserve to divide it into triangles, understanding that all triangles have internal angles that sum up come $180°$. Climate multiply the number of triangles by $180°$ and also finally division by the variety of vertices the the polygon to gain the worth of its inner angle. This won’t it is in as difficult as that sounds, an especially once us start illustration the triangle on our figure.

Solve the Question

First, let’s attract triangles beginning at one peak in our figure, prefer this:

So right here we can see the the amount of all of the inner angles in our polygon can be represented as 7 triangles. To discover the worth of an interior angle in ~ this polygon, we have the right to just multiply the variety of triangles through $180°$, then divide by the number of internal angles, i m sorry 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°$

Excellent! therefore the internal angle that a $9$-sided polygon is $140°$. We have the right to see the $x$ and also one interior angle lied on the very same side of a right line, so their sum must be $180°$. Therefore $x=180°-140°$, or $x=40°$.

The correct answer is $40°$.

What Did we Learn

Now us know exactly how to find the interior angle for any kind of regular polygon. We can just divide it right into triangles, get the complete sum the the interior angles the the polygon by multiplying the variety of triangles through $180°$, then dividing this amount by the number of vertices of the polygon (which is additionally equal to the number of sides that the polygon).

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