The sum of the measures of the exterior angles of any polygon is a fascinating geometric fact that applies regardless of the number of sides the polygon has. For any polygon, including a decagon (which has 10 sides), the sum of the exterior angles is always 360 degrees.
To understand why this is the case, it’s helpful to consider how exterior angles are formed. An exterior angle is created when you extend one side of the polygon at a vertex. When you do this for all the vertices of the polygon, you’ll find that as you turn around the polygon, you will make a complete revolution. This complete turn represents 360 degrees.
Therefore, even though a decagon has 10 sides and 10 vertices, the total measurement of its exterior angles will still add up to 360 degrees. This is a key property in geometry that holds true for polygons of any number of sides.
In conclusion, irrespective of the shape or size of the decagon, the sum of the measures of the exterior angles remains a constant 360 degrees.