Name a pair of adjacent angles. explain why they are adjacent. name a pair of acute vertical angles. name a pair of supplementary angles.

The 41° and the 90° are adjacent.  They are adjacent because they are touching each other side by side.  That is the angles SUR and SUT

Angle SUR is acute, because it is 41° and it less than 90°.  Same as angle  PUQ. Angle PUR = Angle SUR, both are vertically opposite, therefore PUR is also 41°. 

Angles TUQ and QUN are both supplementary because they both add up to 180°, which is the straight line TUN.