What is the sum of the exterior angle measures, one at each vertex, of this polygon?
Understand the Problem
The question is asking for the sum of the exterior angle measures of a polygon, specifically a hexagon, which is significant in geometry as it involves understanding the properties of polygons.
Answer
The sum of the exterior angle measures is $360^\circ$.
Answer for screen readers
The sum of the exterior angle measures of this hexagon is $360^\circ$.
Steps to Solve
- Identify the number of sides in the polygon
The given polygon is a hexagon, which has 6 sides.
- Understand the formula for the sum of exterior angles
The sum of the exterior angle measures of any convex polygon is always $360^\circ$.
- Apply the formula
Since the polygon is a hexagon, we directly apply the formula: $$ \text{Sum of exterior angles} = 360^\circ $$
The sum of the exterior angle measures of this hexagon is $360^\circ$.
More Information
This result applies to all convex polygons, regardless of the number of sides. Thus, whether the polygon has three, six, or any other number of sides, the total sum of the exterior angles remains constant at $360^\circ$.
Tips
- Confusing interior angles for exterior angles: Remember that the sum of exterior angles is always $360^\circ$, regardless of the number of sides in the polygon.
- Failing to recognize that the sum does not depend on the size or shape of the polygon: It's a universal fact for all convex polygons.
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