Calculate the angle between the two lines.

Step 1: Calculate the angle between the two lines. The first line is given in parametric form: $\vec{r} = (1, 2) + k(1, 2)$. Its direction vector is $\vec{d_1} = (1, 2)$. The second line is given by the equation $2x + y + 5 = 0$. Its normal vector is $\vec{n_2} = (2, 1)$. The direction vector for the second line can be found by taking $(-B, A)$ from $Ax+By+C=0$, so $\vec{d_2} = (-1, 2)$.

The angle $\theta$ between two lines with direction vectors $\vec{d_1