Question

What is the formula for finding the exterior and interior angles of a regular polygon?

Answer 1

Step 1: Determine the formula for the interior angle of a regular polynomial.

The sum of angles of a polynomial is $180\left(n-2\right)°$, where $n$ is the number of sides.

As the polygon is a regular polygon, it will have $n$ equal angles.

So, the measure of each angle is:

$\frac{180\left(n-2\right)°}{n}=180°-\frac{360°}{n}$

Step 2: Determine the formula for the exterior angle of a regular polynomial.

The sum of the interior and the corresponding exterior angle of the polygon must be $180°$ as they form the straight angle.

So, subtract the measure of interior angle from $180°$:

$180°-180°+\frac{360°}{n}=\frac{360°}{n}$

So, the measure of the exterior angle of a regular polygon is $\frac{360°}{n}$.

Therefore, The formula for finding the exterior angle of a regular polygon is $\frac{360°}{n}$ and the interior angles of a regular polygon$180°-\frac{360°}{n}$