Two forces of 8 N and 5 N act on the same small ring…

Step 1. Largest and smallest. The same direction: $8\ \text{N} + 5\ \text{N} = 13\ \text{N}$. Opposite directions: $8\ \text{N} - 5\ \text{N} = 3\ \text{N}$.

Step 2. 4 N or 15 N? Any size from $3\ \text{N}$ to $13\ \text{N}$ is possible, so $4\ \text{N}$ is possible. $15\ \text{N}$ is more than $13\ \text{N}$, so it is not.

Step 3. The angle for 7 N. $(7\ \text{N})^2 = (8\ \text{N})^2 + (5\ \text{N})^2 + 2 \times 8\ \text{N} \times 5\ \text{N} \times \cos\theta$, so $80\ \text{N}^2 \times \cos\theta = -40\ \text{N}^2$ and $\cos\theta = -0.5$. So $\theta = 120^\circ$.