The angle between the lines $x=\mathrm{y}, \mathrm{z}=0$ and $\mathrm{y}=0, \mathrm{z}=0$ is

The angle between two lines can be determined by the angle between their direction vectors.

Line $x=y$, $z=0$ has direction vector $\mathrm{d}_1 = \langle 1, 1, 0 \rangle$.

Line $y=0$, $z=0$ (the $x$-axis) has direction vector $\mathrm{d}_2 = \langle 1, 0, 0 \rangle$.

The cosine of the angle $\theta$ satisfies $\cos \theta = \frac{|\mathrm{d}_1 \cdot \mathrm{d}_2|}{\|\mathrm{d}_1\| \cdot \|\mathrm{d}_2\|}$.

Compute the dot product: $\mathrm{d}_1 \cdot \mathrm{d}_2 = 1 \cdot 1 + 1 \cdot 0 + 0 \cdot 0 = 1$.

Compute magnitudes: $\|\mathrm{d}_1\| = \sqrt{1^2 + 1^2 + 0^2} = \sqrt{2}$, $\|\mathrm{d}_2\| = \sqrt{1^2 + 0^2 + 0^2} = 1$.

So $\cos \theta = \frac{1}{\sqrt{2} \cdot 1} = \frac{1}{\sqrt{2}}$, giving $\theta = rccos\left(\frac{1}{\sqrt{2}}\right) = 45^{\circ}$.

The angle between the lines is $45^{\circ}$.

The correct choice is $\boxed{\text{B}}$.