Using Newton's second law, the car is experiencing a net force parallel to the banked curve such that
[tex]mg \sin(\theta) = \dfrac{mv^2}r \implies \sin(\theta) = \dfrac{v^2}{rg}[/tex]
where [tex]v[/tex] is the tangential speed of the car and [tex]r[/tex] is the radius of the curve. Solve for [tex]\theta[/tex] :
[tex]\sin(\theta) = \dfrac{\left(61.0\frac{\rm m}{\rm s}\right)^2}{(1860\,\mathrm m)g} \approx 0.204 \implies \theta = \sin^{-1}(0.204) \approx \boxed{11.8^\circ}[/tex]
