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 $n=\boxed{15}$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
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?
test