#1 Regular Polygons, interior and exterior angles

A regular polygon is a polygon with all sides and all angles equal.

The sum of the interior angles of a polygon with n sides is given by the formula: $$(n - 2) \times 180^\text{°}$$ .

The polygon has 7 sides.

The measure of each interior angle of a regular polygon with n sides is given by: $$\frac{(n - 2) \times 180^\text{°}}{n}$$ .

The measure of the central angle of a regular polygon with n sides is given by: $$\frac{360^\text{°}}{n}$$ .

An apothem is the line from the center of the polygon to the midpoint of one of its sides.

The area of a regular polygon can be calculated using the formula: $$\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}$$ .

As the number of sides increases, the sum of the interior angles also increases according to the formula: $$(n - 2) \times 180^\text{°}$$ .

The area is $$150\text{√}3 \text{cm}^2$$ .

The measure of the central angle of a regular octagon is $$45^\text{°}$$ .