A 17-year-old Prince George's County high school student who apparently had been sexually assaulted was found beaten to death yesterday behind a Southwest Washington service station, D.C. police reported.

Police identified the victim as Shirley Darlene Gibson of Temple Hills.

Her body was clad only in a jacket, according to witnesses who discovered it at 6 a.m. in the rear of the Gulf station at Fourth and E streets SW. She had been beaten about the head with an object that police declined to discuss.

According to police, the girl, an 11th grader at Potomac Senior High School in Oxon Hill, had been reported missing to Prince George's County police about 2:45 a.m. yesterday by her brother when she did not return home after work.

Terry Blalock, assistant manager of a hamburger carryout on Silver Hill Road where Gibson was employed, said the victim had left work about 8 p.m. Wednesday. She said Gibson usually walked home or rode in a taxi whenever she was not picked up by a family member. She said she did not know how Gibson planned to get home Wednesday.

"She was a very nice girl," said Blalock, who said Gibson had worked for a year at the carryout. "She was very friendly."

Gibson's body was found by a trash man who was working in the rear of the service station, witnesses said. Her body was lying on the cement pavement. A tire rim, which police later confiscated, was near her body, witnesses said. a

Police said last night they had neither suspects nor motive in the slaying.

Gibson, described by her family as "strong, sensitive and serious," had worked at the hamburger shop primarily to earn money to attend college.

"She knew what she wanted out of life," said her sister-in-law, Cynthia Gibson, 23. "She wanted to be a teacher for the retarded, that was her goal. gShe had a brother who was retarded and she wanted to help others like him.

"Shirley was not a regular teen-ager who spent her time out of the house. She wanted to be here to help me. We have two small children, and she was more like a sister to them than an aunt."