\frac14
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
In the diagram, $BP$ and $BQ$ trisect $\angle ABC$. $BM$ bisects $\angle PBQ$. Find the ratio of the measure of $\angle MBQ$ to the measure of $\angle ABQ$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac14
In the diagram, $BP$ and $BQ$ trisect $\angle ABC$. $BM$ bisects $\angle PBQ$. Find the ratio of the measure of $\angle MBQ$ to the measure of $\angle ABQ$.
train