The angle between an incident ray and the reflected ray is $70^{\circ}$ as shown in the figure. What is the value of $\theta$?

$(55^{\circ})$ According to the law of reflection, the angle of incidence $(i)$ is equal to the angle of reflection $(r)$.
Given that the total angle between the incident ray and the reflected ray is $70^{\circ}$, we have $i + r = 70^{\circ}$.
Since $i = r$, we can write $2i = 70^{\circ}$, which gives $i = 35^{\circ}$.
The normal to the mirror surface makes an angle of $90^{\circ}$ with the mirror.
Therefore, the angle $\theta$ between the incident ray and the mirror surface is $\theta = 90^{\circ} - i$.
Substituting the value of $i$, we get $\theta = 90^{\circ} - 35^{\circ} = 55^{\circ}$.