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?
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 $n=\boxed{15}$.