Answer
$71.57^{\circ}$
Work Step by Step
We see that the initial point is: $(1,5)$. The ending point is: $(2,4)$.
So, $\vec{w} =(2-1)\vec{i}+(4-5) \vec{j}=\vec{i}-\vec{j}$ and $\vec{v}=(5-3)\vec{i}+(5-4) \vec{j}=2\vec{i}+\vec{j}$
Now, the angle between two vectors can be computed as:
$\cos \theta =\dfrac{\vec{v} \cdot \vec{w}}{|v||w|}=\dfrac{(\vec{i}-\vec{j}) (2\vec{i}+\vec{j})}{(\sqrt {1+1})(\sqrt {4+1})}\\=\dfrac{1}{\sqrt {10}}$
Therefore, $\theta =\cos^{-1}(\dfrac{1}{\sqrt 2})=71.57^{\circ}$