Answer
$14.04^{\circ}$
Work Step by Step
We're given that,
$\vec{a} = (3\,m)\hat{i} + (4\,m)\hat{j}$ and $\vec{b} = (5\,m)\hat{i} + (-2\,m)\hat{j}$.
We can add these vectors component-wise:
$\vec{a}+\vec{b} = (3\,m+5\,m)\hat{i} + (4\,m-2\,m)\hat{j} = 8\,m\,\hat{i}+2\,m\,\hat{j}$.
The angle then equals:
$tan^{-1}(\frac{2\,m}{8\,m}) = 14.04^{\circ}$.
This is our final answer since we take the angle between the vector and $\hat{i}$ (the positive x axis) by default.
