Angelucci was elected in a 4-3 vote with board members Scott Sweeney, David Morgan and Brad Wheeler voting against her.
Morgan wanted Wheeler to be chairman, but after nominating him, Wheeler only drew votes from Morgan, Sweeney and himself.
Banks was reluctant to explain his support for Angelucci after the meeting.
“I felt like it was the best option,” he said, declining to say more.
Wheeler also struck out in serving as this year’s vice chairman after being nominated by Sweeney.
The board elected outgoing chairman Randy Scamihorn to the spot in a 6-1 vote with Sweeney opposed.
“It is what it is,” Wheeler said after the meeting.
A Republican fiscal conservative, Angelucci was elected to the board in November 2010 after closely following the school district as a parent for years.
Critics say her reputation for thoroughly researching the issues and questioning administrators rather than rubber stamping whatever Superintendent Michael Hinojosa proposes has not made her one of his favorite board members.
In facing a budget shortfall, her preference is to cut central office administrators rather than classroom teachers. She also led the charge to recently rewrite the district’s staff discipline policy to help give teachers more of a voice during disciplinary actions.
“I will do everything in my power to do the best job that I can,” Angelucci told her colleagues.
She stressed her intentions to keep the board unified and acting “as a team,” through the coming year.
The chair and vice chair will each serve a one-year term, which will end in January 2015.
Wheeler said he was not disappointed with how the votes were drawn.
“I don’t have anything against anybody,” he said after the meeting. “That’s what the board members decided, and that’s what it was. They are good people and hopefully we can go forward and continue to make progress.”