# what is the name of a 9 sided polygon

The determine above exhibits an everyday 9-sided polygon. What’s the worth of \$x\$ ?

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## Survey the Query

Let’s search the issue for clues as to what it is going to be testing, as it will assist shift our minds to consider what sort of math data we’ll use to resolve this query. Take note of any phrases that sound math-specific and something particular about what the numbers appear like, and mark them on our paper.

Let’s maintain what we’ve realized about this ability on the tip of our minds as we method this query.

## What Do We Know?

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Let’s fastidiously learn via the query and make a listing of the issues that we all know.

1. We now have an everyday \$9\$-sided polygon
2. We wish to know the worth of an exterior angle to that polygon proven within the determine

## Develop a Plan

We all know that the sum of angles on one aspect of a straight line is \$180°\$ from the determine, we will see that if we will discover the worth of the inside angle at one vertex of the polygon, then we will subtract that worth from \$180°\$ to get the worth of \$x\$.

To search out the inside angle of any polygon, we will divide it into triangles, figuring out that every one triangles have inner angles that sum as much as \$180°\$. Then multiply the variety of triangles by \$180°\$ and eventually divide by the variety of vertices of the polygon to get the worth of its inside angle. This gained’t be as tough because it sounds, notably as soon as we begin drawing the triangles on our determine.

## Clear up the Query

First, let’s draw triangles beginning at one vertex in our determine, like this:

So right here we will see that the sum of all the inner angles in our polygon will be represented as seven triangles. To search out the worth of an inner angle inside this polygon, we will simply multiply the variety of triangles by \$180°\$, then divide by the variety of inner angles, which is 9. \$Inside Angle of a Polygon\$ \$=\$ \${180°·Variety of Triangles}/{Variety of Vertices}\$ \$ \$ \$ \$ \$Inside Angle of a Polygon\$ \$=\$ \${180°·7}/9\$ \$ \$ \$ \$ \$Inside Angle of a Polygon\$ \$=\$ \${9·20°·7}/9\$ \$ \$ \$ \$ \$Inside Angle of a Polygon\$ \$=\$ \$20°·7\$ \$ \$ \$ \$ \$Inside Angle of a Polygon\$ \$=\$ \$140°\$

Wonderful! So the inside angle of a \$9\$-sided polygon is \$140°\$. We will see that \$x\$ and one inside angle lie on the identical aspect of a straight line, so their sum should be \$180°\$. So \$x=180°-140°\$, or \$x=40°\$.

## What Did We Study

Now we all know precisely how one can discover the inside angle for any common polygon. We will simply divide it into triangles, get the entire sum of the inside angles of the polygon by multiplying the variety of triangles by \$180°\$, then dividing this sum by the variety of vertices of the polygon (which can be equal to the variety of sides of the polygon).

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