Angle between two lines

[burgerandcheese]

I drew the angles in red, purple, blue and green. Which angle is the one we're finding here?
Using the dot product, θ ≈ 34.6°. AS and UR are skew lines. If they are skew lines then how come there's an angle between them?

Thank you in advance

 

[Dr.Peterson]

What you marked in color are not angles at all.

What they want is the angle between AS and a line through A parallel to UR. That is, it is the angle between the directions of those lines.