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Equiangular Polygon Sums - Concept
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The sum of the angles in a polygon is always equal to the number of sides in a polygon minus two, all multiplied by 180. Since the angles in an **equiangular polygon** are equal, the measure of one angle in any equiangular or regular polygon is simply the sum of polygon angles divided by the number of angles in the polygon. Knowing this information allows us to solve polygon problems with missing angle measurements.

Let's say I tell you, you have ten-sided

figure it's eqiangular.

What's going to be the measure

of one of those angles.

To find that out we have

to first back up.

There's two key terms.

equiangular and regular that are going

to apply to what we're talking about here.

The first one is equiangular which means

that all the angles in the polygon

are congruent.

It doesn't have to do anything

with the sides. It just means the angles.

You can remind yourself of that because

it look like we have the word angle

here.

Regular combines equilateral

and equiangular.

It says that all angles and all sides

must be congruent to each other.

So we look at these two

polygons right here.

We have two pentagons, only one

of these are equiangular.

Well, here we have all sides

marked as congruent. So this is not equiangular.

If we look at this pentagon right here, all

of your angles are marked as congruent

to each other.

So, yes, this one would be equiangular.

If you put these together, you have a regular

polygon, which is like this hexagon

right here.

Notice that all the sides are congruent

to each other, and all the angles are

congruent to each other.

But how do we calculate the measure

of one of those angles?

Well, to do that we need to look

at our polygon angle sum.

We said that the sum of the angles in

a polygon is equal to N minus 2 times

180. To find that, we said how many triangles

can we draw in a polygon.

And that was always the number of sides

minus 2. The sum of the angles

in the triangle is 180.

So if you want to find just one angle

in a regular polygon, you're going to

take this formula, which is the quantity

of N minus 2, times 180, and

since all the angles are the same, you

can just divide by the number of

angles that you have.

So you're taking this formula and you're

dividing by the number of sides that

you have in your equiangular polygon

or in your regular polygon.

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