Triangle abc has side lengths: √6, √2, and 2√2 units. the measures of the angles of the triangle are a: 25,75,80 b: 45,45,90 c: 30,60,90 if the base of the triangle has a length of √6 then the measure of the base angle is a: 30 b: 90 c: 25 d: 80 e: 60 f: 45

The ratios of side lengths are 1 : √3 : 2, characteristic of a 30-60-90 right triangle.

The measures of the angles are ...
  C: 30, 60, 90

The angles at either end of the middle length are those that are shortest and longest, 30 and 90. (The middle size angle is opposite the middle length side.) Which of these you call the "base angle" is up to you. Perhaps the choice being sought is ...
  A: 30