If the degree measure of an arc of a circle is increased by $20\%$ and the radius of the circle is increased by $25\%$, by what percent does the length of the arc increase?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If the degree measure of an arc of a circle is increased by $20\%$ and the radius of the circle is increased by $25\%$, by what percent does the length of the arc increase?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
50
If the degree measure of an arc of a circle is increased by $20\%$ and the radius of the circle is increased by $25\%$, by what percent does the length of the arc increase?
train