How to find each exterior angle of a polygon?
Understand the Problem
The question is asking for the method to calculate the exterior angles of a polygon. Exterior angles can be determined by dividing 360 degrees by the number of sides of the polygon.
Answer
The measure of each exterior angle is given by $ \frac{360}{n} $ where $ n $ is the number of sides of the polygon.
Answer for screen readers
The measure of each exterior angle of a polygon is calculated using the formula:
$$ \text{Exterior Angle} = \frac{360}{n} $$
where ( n ) is the number of sides.
Steps to Solve
- Identify the number of sides of the polygon
First, determine how many sides (n) the polygon has. This is essential because the formula for calculating exterior angles depends on the number of sides.
- Apply the exterior angle formula
Use the formula to calculate the measure of each exterior angle:
$$ \text{Exterior Angle} = \frac{360}{n} $$
where ( n ) is the number of sides of the polygon.
- Calculate the exterior angle
Substitute the identified number of sides into the formula to find the measure of each exterior angle. For example, if the polygon has 5 sides:
$$ \text{Exterior Angle} = \frac{360}{5} = 72 \text{ degrees} $$
- Verify your calculation
It's a good practice to check your calculation by ensuring that all the exterior angles add up to 360 degrees. Since all exterior angles are equal in a regular polygon, you can multiply the calculated exterior angle by the number of sides:
$$ n \times \text{Exterior Angle} = 360 $$
For example, for a 5-sided polygon:
$$ 5 \times 72 = 360 \text{ degrees} $$
The measure of each exterior angle of a polygon is calculated using the formula:
$$ \text{Exterior Angle} = \frac{360}{n} $$
where ( n ) is the number of sides.
More Information
The concept of exterior angles is crucial in geometry. In any polygon, the sum of the exterior angles is always 360 degrees, regardless of the number of sides. This property is what simplifies the calculation method.
Tips
- Not identifying the number of sides accurately, which can lead to wrong calculations.
- Forgetting that the polygon must be regular to apply this formula correctly. If the polygon is irregular, the angles will vary.
- Failing to verify the final answer by checking if the total sum of the exterior angles equals 360 degrees.