The Fairfax County school board voted last night to make the Jan. 15 birthday of the Rev. Dr. Martin Luther King Jr. a county school holiday starting next year.

The action does not add an additional school holiday but shifts to Jan. 15 the existing Jan. 18 state holiday observance of the birthdays of Stonewall Jackson and Robert E. Lee.

The vote makes the 15th the observance for all three men, at least for county schools. State and county offices will continue to close on Jan. 18.

Virginia Gov. John N. Dalton recently vetoed a bill that would have made the civil rights leader's birthday a state holiday.

The vote came after a divided school board vote on when to begin and end the next school year. The board narrowly defeated a staff proposal to open the schools Aug. 31, the earliest date ever proposed and one that has brought complaints from parents whose family vacations do not end until Labor Day.

The August opening was recommended to end the late June school closings the schools have been forced to observe for several years in order to include the mandated 180 school days, 10 teacher work days and numerous holidays and vacations.

The board also received a recommendation to liberalize the existing high school sex education course to include discussion of birth control and permit teachers to answer questions on other now-forbidden topics -- homosexuality, abortion, masturbation, rape and incest.

The course would be included as part of the elective biology course that about 90 percent of the county's 60,000 high school students now take. However, any student who elects to take biology could ask to be included in a section that would not discuss sex. Less than 2 percent of high school students now take the expurgated, after-school course now offered on sex education.

The school board will hold a public hearing on the controversial sex education course on May 17 and the school staff will give presentations on the courst at different area offices between April 13 and May 11.