Polygon Angle Sum Theorem

The Polygon Angle Sum Theorem states that the sum of the interior angles of a polygon with n sides is given by the formula: $$(n - 2) \times 180^\text{o}$$ .

To find the measure of one exterior angle of a regular polygon, use the formula: $$\frac{360^\text{o}}{n}$$ , where n is the number of sides.

The measure of one interior angle of a regular polygon can be found using the formula: $$\frac{(n - 2) \times 180^\text{o}}{n}$$ .

The sum of the interior angles of a decagon (10 sides) is $$(10 - 2) \times 180^\text{o} = 1440^\text{o}$$ .

In the Polygon Interior Angle Sum Theorem, n represents the number of sides of the polygon.

The measure of one interior angle in a regular hexagon is $$\frac{(6 - 2) \times 180^\text{o}}{6} = 120^\text{o}$$ .

The measure of one exterior angle of a regular octagon is $$\frac{360^\text{o}}{8} = 45^\text{o}$$ .

If the sum of the interior angles is 720°, the polygon has 5 sides (pentagon), since $$720 = (n - 2) \times 180$$ .

The interior and exterior angles of a polygon are supplementary, meaning they add up to 180°.

The sum of the interior angles of a dodecagon is $$(12 - 2) \times 180^\text{o} = 1800^\text{o}$$ .