The Arlington County Board adopted a $180.4 million budget last night, but not before its Republican-backed majority clashed heatedly with the county Board of Education.

"I'm very disappointed," said Ann Broder, chairman of the school board, which has a Democratic-backed majority, after the county board cut $1.2 million from the proposed school budget. The final school budget was set at $57 million. "It's not a case of poverty, it's a case of priorities," she declared.

The dispute between the school and county boards last night, witnessed by more than 130 partisan spectators, centered on a proposed 10.5 percent pay raise that the school board recommended for its employees. The cuts made by the county board equaled a 2 percent drop in that pay raise, bringing it in line with the 8.5 percent raise the county board will give nonschool county employes.

"One of the biggest problems we have here in terms of the budget review is that past policy has been that we try to have pay treatment equal for both county and school employees." said Walter Frankland, the county board chairman.

The school board is not obligated to limit the raises it gives to 8.5 percent. Board members said programs could be cut to provide money for higher salaries.

The school board will hold hearings before making a final decision on how to spend the money allotted by the county board.