Prosecutors on Tuesday filed a formal rape charge against a 47-year-old Douglas County man who was arrested Monday afternoon.

The victim, a 29-year-old woman, reported the rape to sheriff’s deputies shortly after 3 a.m. Monday, and the man was arrested later that day. She said the incident happened at a home in the 1000 block of 1369 Road.

The victim was known to the suspect, said Lt. Kari Wempe, a sheriff’s spokeswoman.