How to find one exterior angle of a polygon?
Understand the Problem
The question is asking how to calculate one exterior angle of a polygon. The approach involves knowing the number of sides of the polygon, as the measure of each exterior angle in a regular polygon can be found using the formula 360 degrees divided by the number of sides.
Answer
The measure of one exterior angle is $\frac{360^\circ}{n}$.
Answer for screen readers
The measure of one exterior angle of a regular polygon with $n$ sides is given by $$ \frac{360^\circ}{n} $$.
Steps to Solve
-
Identify the Number of Sides Determine how many sides the polygon has. Let’s represent this number as $n$.
-
Use the Exterior Angle Formula The formula for calculating one exterior angle of a regular polygon is given by: $$ \text{Exterior Angle} = \frac{360^\circ}{n} $$ This means you will divide 360 degrees by the number of sides.
-
Calculate the Exterior Angle Substituting the value of $n$ (the number of sides) into the formula will give you the measure of one exterior angle.
The measure of one exterior angle of a regular polygon with $n$ sides is given by $$ \frac{360^\circ}{n} $$.
More Information
For regular polygons, all exterior angles are equal, and they sum up to 360 degrees regardless of the number of sides. This means that if you have a polygon with many sides, the exterior angles will be relatively small, but they will always add up to a full circle.
Tips
- Confusing exterior angles with interior angles: Always remember that exterior angles are formed outside the polygon and are supplementary to the interior angles.
- Using the formula incorrectly: Make sure to always divide 360 degrees by the correct number of sides $n$.
