To determine the sum of the measures of the exterior angles of any convex polygon, we can follow these concepts and conclusions:
### Understanding Exterior Angles of a Polygon
1. Definition: Exterior angles are the angles formed between any side of a polygon and the extension of its adjacent side.
2. Properties:
- Each exterior angle of a polygon is supplementary to its respective interior angle.
- When a polygon is convex, all its interior angles are less than [tex]\(180^{\circ}\)[/tex], which ensures that the polygon doesn't "cave-in" or curve inward.
### Key Concept
- Sum of Exterior Angles: The exterior angles of a convex polygon, one at each vertex, always add up to a constant value.
### Explanation
Regardless of the number of sides of the polygon, whether it is a triangle (3 sides), a quadrilateral (4 sides), a pentagon (5 sides), or any [tex]\(n\)[/tex]-sided polygon, the sum of all the exterior angles is always the same.
To picture this:
- Imagine walking around the perimeter of the polygon. At each vertex, you turn at the exterior angle to head towards the next side.
- After completing a full loop around the polygon, you will have made one complete turn (360 degrees).
### Conclusion
Thus, the sum of the measures of the exterior angles of any convex polygon is always:
[tex]\[ 360^{\circ} \][/tex]
Therefore, the correct answer is:
B. [tex]\( 360^{\circ} \)[/tex]
