Find the smallest positive integer $x$ (measured in degrees) such that
\[\tan (x - 160^{\circ}) = \frac{\cos50^{\circ}}{1 - \sin50^{\circ}}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the smallest positive integer $x$ (measured in degrees) such that
\[\tan (x - 160^{\circ}) = \frac{\cos50^{\circ}}{1 - \sin50^{\circ}}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
50^\circ
Find the smallest positive integer $x$ (measured in degrees) such that
\[\tan (x - 160^{\circ}) = \frac{\cos50^{\circ}}{1 - \sin50^{\circ}}.\]
train