In a move that irritated the Republican-backed majority on the Arlington County Board, School Board Chairman Mary Margaret Whipple announced yesterday that she will run for the County Board.

Whipple, 38, who said she would remain on the school board through the campaign, said she was the first school board member to seek an elective political office in Arlington. She said she will seek Democratic endorsement for the seat.

County Board Chairman Dorothy Grotos, a Republican who has already announced she is seeking reelection in the November election, said she found it "interesting that the Democrats went to a school board member" to find a County Board candidate. "They must have been really looking for candidates," Grotos said.

Whipple joins Charles Rinker, 38, a iliaison officer for Action, a federal agency, in seeking the endorsement of the Democratic Party and the Arlingtonians for Better Government.

Whipple said she was "distressed" by the County Board majority's "attitude toward the schools. Next year the County Board has the opportunity of appointing two new people to the school board. If a Republican backed) majority were on the board, it would make a difference in the way the schools are going," she said.

Grotos, who voted against Whipple's school board appointment three years ago, said she was "surprised" at Whipple's challenge. "There's a lot more to a County Board job than the schools," Grotos said.