How to find each interior angle of a polygon?
Understand the Problem
The question is asking how to calculate the measure of each interior angle of a polygon, which involves using the formula for the interior angles depending on the number of sides the polygon has.
Answer
The measure of each interior angle of a regular polygon is given by the formula $ \frac{(n - 2) \times 180^\circ}{n} $.
Answer for screen readers
The measure of each interior angle of a regular polygon is given by the formula:
$$ \frac{(n - 2) \times 180^\circ}{n} $$
Steps to Solve
- Identify the number of sides of the polygon
To calculate the measure of each interior angle, we first need to know how many sides the polygon has. Letâ€™s denote the number of sides as $n$.
- Use the formula for sum of interior angles
The sum of the interior angles of a polygon can be calculated using the formula:
$$ S = (n - 2) \times 180^\circ $$
where $S$ is the sum of the interior angles and $n$ is the number of sides.
- Calculate the measure of each interior angle
To find the measure of each interior angle in a regular polygon (where all angles are equal), divide the sum of the interior angles by the number of sides:
$$ \text{Measure of each interior angle} = \frac{S}{n} = \frac{(n - 2) \times 180^\circ}{n} $$
The measure of each interior angle of a regular polygon is given by the formula:
$$ \frac{(n - 2) \times 180^\circ}{n} $$
More Information
This formula shows that as the number of sides $n$ increases, the measure of each interior angle approaches $180^\circ$, which is the angle in a straight line. For example, a triangle ($n = 3$) has angles of $60^\circ$, while a regular hexagon ($n = 6$) has angles of $120^\circ$.
Tips
- A common mistake is forgetting to properly substitute the number of sides $n$ into the formulas.
- Confusing the formulas for the sum of exterior angles and interior angles; remember that the sum of exterior angles of any polygon is always $360^\circ$.