What is the sum of the exterior angles of an octagon?
Understand the Problem
The question is asking for the calculation of the sum of the exterior angles of an octagon. In general, the sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides. This can be used to provide a complete answer.
Answer
$360$ degrees
Answer for screen readers
The sum of the exterior angles of an octagon is $360$ degrees.
Steps to Solve
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Identify the property of exterior angles The sum of the exterior angles of any polygon is always equal to 360 degrees. This is a theorem in geometry that applies to all polygons.
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Calculate for the octagon Since the octagon is a polygon with 8 sides, we still use the same property.
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Conclude the sum of the exterior angles Thus, for the octagon, the sum of the exterior angles is:
$$ 360 \text{ degrees} $$
The sum of the exterior angles of an octagon is $360$ degrees.
More Information
This property holds true for all polygons, which makes it a valuable rule in geometry. It simplifies many geometric calculations since you don't have to consider the number of sides.
Tips
- A common mistake is to think that the sum depends on the number of sides. Remember, it's always $360$ degrees for any polygon, not just octagons.
