How do you calculate the interior angle of a regular polygon?

To calculate the interior angle of a regular polygon, use the formula: \((n-2) \times 180^\circ / n\).

A regular polygon is a shape with all sides and angles equal. The formula \((n-2) \times 180^\circ / n\) helps you find the measure of each interior angle, where \(n\) is the number of sides. This formula works because the sum of the interior angles of any polygon is \((n-2) \times 180^\circ\). For example, a triangle (3 sides) has interior angles summing to \(180^\circ\), a quadrilateral (4 sides) sums to \(360^\circ\), and so on.

To break it down, first calculate the total sum of all interior angles by multiplying \((n-2)\) by \(180^\circ\). This step gives you the sum of all the angles inside the polygon. Next, divide this sum by the number of sides \(n\) to find the measure of each individual angle.

For instance, if you have a regular hexagon (6 sides), you would first calculate the total sum of the interior angles: \((6-2) \times 180^\circ = 720^\circ\). Then, divide this sum by the number of sides: \(720^\circ / 6 = 120^\circ\). Therefore, each interior angle of a regular hexagon is \(120^\circ\).

This method ensures you can find the interior angle of any regular polygon, making it a handy tool for solving geometry problems.