Problem: A compound curve consists of two circular curves. The central angle of the first curve ($I_1$) is $30^\circ$ and the central angle of the second curve ($I_2$) is $45^\circ$. What is the total intersection angle ($I$) of the compound curve?

Problem: A symmetrical compound curve has a total intersection angle $I = 60^\circ$. Both constituent curves have equal central angles. If the radius of the first curve ($R_1$) is 400 m and the radius of the second curve ($R_2$) is 600 m, find the central angles $I_1$ and $I_2$.

Problem: A compound curve is designed with a total intersection angle $I = 85^\circ$. The first curve has a central angle $I_1 = 35^\circ$. Find the central angle of the second curve, $I_2$.

Problem: Two parallel tangents are connected by a reverse curve. The radius of the first curve is $R_1 = 200\text{ m}$ and the second curve has $R_2 = 300\text{ m}$. Both curves have a central angle $I_1 = I_2 = 20^\circ$. Calculate the perpendicular distance $d$ between the parallel tangents.

Problem: A reverse curve connects two parallel tangents separated by a perpendicular distance $d = 25\text{ m}$. The curves have equal radii ($R_1 = R_2 = R$) and equal central angles ($I_1 = I_2 = 15^\circ$). Determine the required radius $R$.

Problem: Two parallel tangents are separated by a perpendicular distance $d = 15\text{ m}$. The reverse curve connecting them has equal radii $R_1 = R_2 = 250\text{ m}$. Find the central angle $I$ ($I_1 = I_2 = I$) of the curves.

Problem: A highway transition curve is designed as an Euler spiral. At a length of $50\text{ m}$ from the TS (Tangent to Spiral), the radius of curvature is $300\text{ m}$. Calculate the spiral constant $K$.

Problem: A spiral curve has a total length $L_s = 120\text{ m}$. It connects a tangent to a simple circular curve that has a radius $R_c = 400\text{ m}$. Determine the spiral angle $\theta_s$ in radians and degrees.

Problem: For a highway curve, a spiral angle of $0.2\text{ radians}$ is required for a smooth transition. The radius of the simple circular curve is $500\text{ m}$. What must be the total length of the spiral $L_s$?