Exterior Angle (Regular)
Measure of one exterior angle of a regular polygon.
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Example
Pentagon: 72°
How it works
In a regular polygon, all sides and all angles are equal, so every exterior angle is the same size. The exterior angles around any polygon add up to 360°, because turning all the way around once makes a full circle; dividing 360° by the number of sides gives one equal exterior angle.
When to use it
Use this when you know a shape is a regular polygon and you need the size of one outside turn at a corner. It is common in geometry problems, angle-chasing, and in design or tiling patterns that use regular shapes.
Worked example, step by step
Find one exterior angle of a regular octagon. Use the formula: θ = 360° / n Substitute n = 8: θ = 360° / 8 Calculate: θ = 45° Final answer: one exterior angle is 45°
Common mistakes to avoid
- Using the formula for an irregular polygon, where the exterior angles may not all be equal
- Dividing by the number of vertices incorrectly when the shape is not regular
- Confusing exterior angle with interior angle and using 180° - θ without checking what is being asked
Did You Know?
The exterior angles of any polygon always sum to exactly 360°, no matter how many sides it has.
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