Prevaricate
Etymology
From Latin praevaricari, "to walk crookedly, deviate," from prae- ("before") plus varicare, "to straddle," from varus, "bent, knock-kneed." It described a plowman who wandered from a straight furrow, and later a lawyer who colluded with the other side. That crooked path became the crooked speech of one who bends away from the plain truth.
verb · /prih-VAIR-ih-kayt/
To speak or act evasively in order to avoid telling the truth.
What it names
The verb for dodging the truth without quite lying — answering a question sideways, hedging, or being deliberately vague.
Example
Pressed on the missing funds, the treasurer prevaricated, offering everything but a straight answer.
Related idea
Lie asserts a falsehood outright; to prevaricate is to evade — twisting and hedging to keep from saying the true thing.