To find an angle with respect to the x-axis or y-axis, one must start from the positive side of the respective axis and measure counterclockwise. When calculating the angle of a vector, such as one pointing 17.1 degrees west of north, the correct approach involves determining the quadrant and adjusting the angle accordingly. For example, to find the angle with respect to the positive x-axis, one should subtract from 180 degrees if the vector is in the second quadrant, resulting in 162.9 degrees. Clarification on what "with respect to positive x-axis" means is essential for accurate calculations. Understanding these principles helps avoid common mistakes in angle measurement.