First, we resolve each force into its horizontal (x) and vertical (y) components. We will measure angles counter-clockwise from the positive x-axis.

To solve this problem, we need to find the resultant force from the three given forces and then determine the magnitude and direction of the force required to keep the system in equilibrium. The equilibrium force will have the same magnitude as the resultant force but act in the opposite direction.

First, we resolve each force into its horizontal (x) and vertical (y) components. We will measure angles counter-clockwise from the positive x-axis.

• Force $F_1$: Magnitude $10 \text{ N}$, Angle $\theta_1 = 30^\circ$.
• Force $F_2$: Magnitude $15 \text{ N}$. The diagram shows it $30^\circ$ from the negative y-axis in the second quadrant. So, its angle from the positive