Washingtonians filed a record number of new claims for jobless benefits last month, even though unemployment offices were closed for several days because of snow and the Christmas holiday. The state Employement Security Department says more than 90,000 people applied for regular unemployment benefits in December. That’s a 75 percent increase over December 2007. The previous record was set in December 2001, when nearly 73,000 people filed jobless claims. The state says its unemployment insurance trust fund has more than $4 billion, making it one of the healthiest in the country. More than 136,000 Washingtonians were getting jobless benefits at the end of 2008. The average weekly payment was about $350.