well, again, recall, there are 180° in π radians, let's now check how many degrees in 1 radian then.
[tex]\bf \begin{array}{ccll}
de grees&radians\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
180&\pi \\
d&1
\end{array}\implies \cfrac{180}{d}=\cfrac{\pi }{1}\implies \cfrac{180\cdot 1}{\pi }=d[/tex]
that many degrees in 1 radian, just 1 radian.
well, how close are their sizes? surely you'd know.