Question

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what is the sum of the exterior angle measures, one at each vertex, of a convex 17 - gon?
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Explanation:

Step1: Recall the exterior angle sum theorem for convex polygons.

For any convex polygon, the sum of the exterior angle measures (one at each vertex) is always \(360^\circ\), regardless of the number of sides \(n\) (where \(n\geq 3\) for a polygon).

Step2: Apply the theorem to a convex 17 - gon.

Since the convex 17 - gon is a convex polygon, by the exterior angle sum theorem, the sum of its exterior angle measures (one at each vertex) is \(360^\circ\).

Answer:

\(360\)