Determine the magnitude of the vector sum Determine the magnitude of the vector sum $V = V1 + V2$ and the angle $θx$ which $V$ makes with the positive x-axis.



I get $B$ to be 37.0414 but I am not sure what to add it do to get the correct angle.
Here's the easiest way: find the components of $V_1$ and $V_2$ explicitly to find $V$.  Once you have the components of $V$, it is easy to get its magnitude and the angle it makes with the $x$-axis.

Let $\theta_1$ be the angle $V_1$ makes with the x axis and $\theta_2$ be the same for $V_2$.

To start, we have
$$
\tan\theta_1=3/6=\frac12
$$
From there, do some quick manipulation to find $\sin\theta_1$ and $\cos\theta_1$.  We have
$$
V_1=(9\cos\theta_1,9\sin\theta_1)=(8.05,4.02)
$$
Now, $V_2$ makes an angle of $180˚-63˚=117˚=\theta_2$ with the x-axis.  So, we have
$$
V_2=(12\cos\theta_2,12\sin\theta_2)=(-5.45,10.69)
$$
From there, we have
$$
V=V_1+V_2=(2.60,14.71)
$$
Now, it's simply a matter of finding
$$
|V|=\sqrt{2.60^2+14.71^2}=14.9\\
\theta_x=\arctan(14.71/2.6)=80˚
$$
The angle is between the two vectors. So it is 

$(90-{\arctan{{\frac{1}{2}}}})+(90-63)$,

such that the ${\arctan{{\frac{1}{2}}}}$ is due to the $v_{1}$