The measure of an interior angle of a regular $n$-gon is $\frac{180(n-2)}{n}$ degrees and the measure of an exterior angle is $\frac{360}{n}$ degrees.  Solving  \[
\frac{180(n-2)}{n}=6.5\cdot\left(\frac{360}{n}\right),
\] we find $n=\boxed{15}$.
Question:
In a regular polygon, the measure of an interior angle is 6.5 times the measure of an exterior angle. How many sides does the polygon have?
Answer:
Let's think step by step.

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15
In a regular polygon, the measure of an interior angle is 6.5 times the measure of an exterior angle. How many sides does the polygon have?
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