To determine the measure of the exterior angle at a vertex of a regular hexagon (a polygon with six sides that has the same interior angle measures), we can follow these steps:
1. **Calculate the measure of each interior angle of a regular hexagon**:
The formula for the interior angle of a regular polygon is given by:
\[
\text{Interior angle} = \frac{(n - 2) \times 180°}{n}
\]
where \(n\) is the number of sides. For a hexagon (\(n = 6\)):
\[
\text{Interior angle} = \frac{(6 - 2) \times 180°}{6} = \frac{4 \times 180°}{6} = \frac{720°}{6} = 120°
\]
2. **Calculate the corresponding exterior angle**:
The exterior angle is supplementary to the interior angle, meaning that:
\[
\text{Exterior angle} = 180° - \text{Interior angle}
\]
Therefore:
\[
\text{Exterior angle} = 180° - 120° = 60°
\]
Hence, the measure of the exterior angle at that vertex is \(60°\).
Final answer: **60°**