Angles in Regular Hexagons and Octagons

A regular polygon is a polygon that is equilateral (all its sides are equal) and equiangular (all its angles are equal).

Angles in regular hexagons:

A six-sided polygon, in which all its sides are equal and whose angles are also equal.

Let's calculate the sum of the angles of a regular hexagon:
We will use the formula that serves to find the sum of the internal angles of a polygon
$180\times (6-2)=$
$180\times 4=720$

Then we will calculate the value of an angle in the regular hexagon:
$720:6=120$
Since all the angles are equal, we only have to divide the total by the number of angles in the regular hexagon.

Pay attention, the sum of the internal angles of any regular hexagon will always be $720^o$, and the size of each angle $120^o$.

Now let's move on to the regular octagon:

A polygon with eight sides, in which all its sides are equal and whose angles are also equal.

Let's calculate the sum of the angles of a regular octagon:
We will use the formula that serves to find the sum of the internal angles of a polygon:
$180\times (8-2)=$
$180\times 6=1080$

Now let's calculate the value of an angle in the regular octagon:
$1080:8=135$

Since all the angles are equal, we only have to divide the total by the number of angles in the regular octagon.

Pay attention, the sum of the internal angles of any regular octagon will always be $1080^o$, and the size of each angle $135^o$.

What the heck is a regular polygon?
A regular polygon is a polygon whose sides and angles are all equal.
How will you remember it?
The word "regular" comes from Latin, where one of its meanings indicates something that is according to the rule, without abrupt changes.
This way you'll remember that in this type of polygons there are no changes in their measurements.

Now let's talk about the internal angles of a regular polygon

As we learned this is the formula to calculate the sum of the internal angles of a polygon:

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

From this formula, it can be deduced that the sum of the internal angles of a polygon depends on the number of edges it has.

All the internal angles of a regular polygon are equal.
Therefore, after discovering the sum of the internal angles of the polygon, we will divide it by the number of edges or sides it has (equal to the number of angles) and we will arrive at the value of each angle.
We can see it in the formula to calculate the size of an internal angle of a regular polygon:

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

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