Noah is designing a polygon with six sides that has the same interior angle measures. At one of the vertices, he extends the line to form an exterior angle. What is the measure of the exterior angle at that vertex?(1 point)

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°**