Mathematics

Degree and radian measure are two ways to describe the same rotation—they're just different units, like miles and kilometers. The key insight is that $180°$ always equals $\pi$ radians, so you can set up a proportion: if $180°$ corresponds to $\pi$ rad, what does $135°$ correspond to? Multiply $135°$ by the conversion factor $\frac{\pi}{180°}$ to flip into radians.

Degree and radian measure are two ways to describe the same rotation—they're just different units, like miles and kilometers. The key insight is that $180°$ always equals $\pi$ radians, so you can set up a proportion: if $180°$ corresponds to $\pi$ rad, what does $135°$ correspond to? Multiply $135°$ by the conversion factor $\frac{\pi}{180°}$ to flip into radians.