The components of vector a⃗ are ax = + 3.90 and ay = - 4.00. What is the angle measured counterclockwise from the + x-axis to vector a⃗?

The angle is the arctangent of the ratio of ay to ax. Since ay is negative and ax is positive, it is a 4th-quadrant angle.

... arctan (ay/ax) = arctan (-4.00/3.90) ≈ 314.27°

... about 5.48513 radians