For a particular circle, a central angle of $75^{\circ}$ will intercept an arc of length $10\pi$ feet. What is the radius of this circle?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
For a particular circle, a central angle of $75^{\circ}$ will intercept an arc of length $10\pi$ feet. What is the radius of this circle?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
24
For a particular circle, a central angle of $75^{\circ}$ will intercept an arc of length $10\pi$ feet. What is the radius of this circle?
train