What is the sum of the exterior angles of an octagon?
Understand the Problem
The question is asking for the sum of the exterior angles of an octagon, which is a polygon with eight sides. The sum of the exterior angles for any polygon can be calculated using the fact that it is always 360 degrees, regardless of the number of sides.
Answer
$360^\circ$
Answer for screen readers
The sum of the exterior angles of an octagon is $360^\circ$.
Steps to Solve
- Identify the property of exterior angles
The sum of the exterior angles of any polygon is always 360 degrees. This holds true regardless of the number of sides the polygon has.
- Apply the rule to the octagon
Since we're dealing with an octagon, which has 8 sides, we can directly use the established rule:
The exterior angles' sum is
$$ 360^\circ $$
for any polygon.
- Conclusion
Therefore, the sum of the exterior angles of an octagon also equals
$$ 360^\circ $$
The sum of the exterior angles of an octagon is $360^\circ$.
More Information
This property of exterior angles can be useful in various fields such as architecture and engineering when designing structures with angular components. It simplifies calculations involving polygons.
Tips
Common mistakes include trying to calculate the exterior angles based on the number of sides or vertices, forgetting that the sum is always constant at 360 degrees. To avoid this, remember the rule for exterior angles holds true regardless of the polygon shape or size.
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