The Counter-Clockwise (CCW) Convention is an agreed-upon method of expressing the direction of a vector as being equal to some counter-clockwise angle of rotation from due East. According to this convention, East is assigned the direction 0°. A vector that starts at East and is rotated in the counter-clockwise direction by a 90° angle would point North. Thus, North is assigned the direction of 90°. By similar reasoning, West is 180° and South is 270°. Vectors lying between these compass directions will have CCW directions that are in between these angle values. For instance, a third quadrant vector lying between West and South would have a CCW direction that is between 180° (for West) and 270° (for South).
In this question, the vector lies between one of the axes. So use an understanding of the compass directions and their respective angle (first paragraph) to help you answer the question. The protractor can be dragged on top of the vector so that the origin of the protractor lies at the tail of the vector; that's the dot ... not the arrowhead. Bold markings are shown every 15°. You can measure from one of the axes to the vector to get the angle that the vector makes with the axes. Then you will have to add or subtract that angle from the CCW direction that is equivalent to that compass direction. For instance, if you measure a second quadrant vector (a North and West vector) to be some angle from West, then you have measured how many degrees rotation less that the vector is from West. You will have to subtract the measured angle from 180°. And if you measure a third quadrant vector (a West and South vector) to be some angle from West, then that describes how many degrees rotation more that the vector is from West. You will then have to add the measured angle to 180°.