A vector has the parts Ax = -3 and Ay = -4…

Step 1. Size. $\sqrt{(-3)^2 + (-4)^2} = \sqrt{25} = 5$.

Step 2. The quarter. $A_x < 0$ and $A_y < 0$, so the arrow points down and to the left. That is the third quarter, between $180^\circ$ and $270^\circ$.

Step 3. The angle. The angle with the $x$ axis is $\tan^{-1}\dfrac{4\ \text{km}}{3\ \text{km}} = 53.1^\circ$. In the third quarter, the angle from $+x$ is $180^\circ + 53.1^\circ = 233.1^\circ$.