# Measurement of an angle of a regular polygon

When you want to discover the size of an angle of a regular polygon easily and quickly, all you have to do is place in this magnificent formula.
$n$ the number of sides of the given regular polygon and immediately, you will discover the measure of the angle!

The formula to find the size of the angles in a regular polygon:

When:
$=n$ number of edges or sides of the polygon

Note:
All sides and all internal angles of a regular polygon are equal.
If you do not remember how to find the measure of a single angle in a regular polygon you can calculate the sum of the internal angles of the polygon, divide it by the number of angles it has and thus arrive at the size of each angle.

The number of edges (or sides) of a regular polygon $=$ the number of angles of a regular polygon $=n$

## The steps to follow to find the size of an angle in a regular polygon

• Count how many sides your regular polygon has. It's helpful to write a number next to each edge to avoid confusion in the count.
• Place the data in the formula, being careful to respect the order of mathematical operations, and find out the measure of the angle in the regular polygon.

### Let's look at an example

Discover the measure of the angle in the following regular polygon:

First, let's count the number of edges the regular polygon has.

We find that $n=5$
We have before our eyes a regular pentagon!

Now, let's place the data in the formula to find the size of the angle in a regular polygon and we will discover its measure:
$\frac{180\cdot(5-2)}{5}=$
$\frac{180\cdot3}{5}=$
$\frac{540}{5}=108$

Notice, in the last simplification, we obtained in the numerator the sum of the internal angles. We divided it by five (the number of angles in the regular polygon) and it gave us that the measure of each angle in the polygon is $108$.

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