Answer: The radian measure of the given angle is [tex]\dfrac{19\pi}{9}~\textup{radian}.[/tex]Step-by-step explanation: We are given to express the following angle in degree measure in radian measure :[tex]\theta=380^\circ.[/tex]We know thatthe relation between degree measure and radian measure of an angle is as follows :[tex]180^\circ=\pi~\textup{radian}.[/tex]So, we have[tex]1^\circ=\dfrac{\pi}{180}~\textup{radian}.[/tex]Therefore, we get[tex]380^\circ=\dfrac{\pi}{180}\times380=\dfrac{19\pi}{9}~\textup{radian}.[/tex]Thus, the required radian measure of the given angle is [tex]\dfrac{19\pi}{9}~\textup{radian}.[/tex]