**Given Information:**

- Initial velocity of the particle, u = 50 m/s
- Height of the wall, h = 20 m
- Time taken to cross the wall, t = 4 seconds

**To find:**

The angle of projection of the particle.

**Assumptions:**

- We will consider the motion of the particle in a vertical plane only, neglecting the effects of air resistance.
- The acceleration due to gravity, g = 9.8 m/s², is constant throughout the motion.
- The particle is projected from the ground level.

**Approach:**

We can solve this problem using the equations of motion in two dimensions.

1. Let's break the initial velocity u into its horizontal and vertical components.
- The horizontal component, uₓ, remains constant throughout the motion, as there is no horizontal acceleration. Therefore, uₓ = u * cosθ, where θ is the angle of projection.
- The vertical component, uᵧ, changes due to the acceleration due to gravity. Therefore, uᵧ = u * sinθ.

2. The time of flight, T, can be calculated using the equation of motion:
- h = uᵧ * t - 0.5 * g * t²

3. We can solve this equation for T by substituting the given values of h, uᵧ, g, and t. This will give us a quadratic equation in T.

4. The horizontal range, R, can be calculated using the equation of motion:
- R = uₓ * T

5. We can solve this equation for R by substituting the given values of uₓ and T.

6. Finally, we can find the angle of projection θ by using the equation:
- θ = tan⁻¹(R/h)

**Calculations:**

1. Finding uₓ and uᵧ:
- uₓ = 50 * cosθ
- uᵧ = 50 * sinθ

2. Finding T:
- h = uᵧ * t - 0.5 * g * t²
- 20 = (50 * sinθ) * 4 - 0.5 * 9.8 * 4²
- 20 = 200 * sinθ - 78.4
- 200 * sinθ = 98.4
- sinθ = 0.492

3. Finding R:
- R = uₓ * T
- R = (50 * cosθ) * T

4. Substituting sinθ = 0.492 and solving for R:
- R = (50 * cos⁻¹(0.492)) * T

5. Substituting T = 4 seconds and solving for R:
- R = (50 * cos⁻¹(0.492)) * 4

6. Finally, finding the angle of projection θ:
- θ = tan⁻¹(R/h)
- θ = tan⁻¹(((50 * cos⁻¹(0.492)) * 4)/20)

**Conclusion:**

By solving the above equation, we can find the angle of projection of the particle.