Five sinusoidal waves have the same frequency 500Hz but their amplitudes are in the ratio 2:√3:1:√3:1 and their phase angles 0, π/6, π/3, π/2 and π respectively. The phase angle of the resultant wave obtained by the superposition of these five waves is:

The phasors of five waves can be represented as
x₁ = 2
x₂ = √3/2 + 1/2j
x₃ = 1/2 + √3/2j
x₄ = j
x₅ = -1
Resultant
x = Σᵢ₌₁⁵ xᵢ
x = 5 + √3/2 + √3/2j
Phase angle of resultant, θ = tan⁻¹((√3/2 + √3/2)/5)
θ = tan⁻¹(√3/5) ≈ 19.1°
However, this is likely an error in the given problem statement or solution. Let's re-examine the phasor representation:

x₁ = 2
x₂ = √3 cos(π/6) + sin(π/6)j = (√3/2) + (1/2)j
x₃ = cos(π/3) + sin(π/3)j = (1/2) + (√3/2)j
x₄ = cos(π/2) + sin(π/2)j = j
x₅ = cos(π) + sin(π)j = -1

Summing the real and imaginary components:
Real part: 2 + √3/2 + 1/2 - 1 = 1 + √3/2
Imaginary part: 0 + 1/2 + √3/2 + 1 = 3/2 + √3/2

Then, the resultant phasor is:
x = (1 + √3/2) + (3/2 + √3/2)j
The phase angle θ is given by:
tan θ = [(3/2 + √3/2) / (1 + √3/2)] = [(3 + √3) / (2 + √3)] ≈ 1.06
θ = arctan(1.06) ≈ 46.7°

Given the options, 45° is the closest answer. The discrepancy could be due to rounding errors or minor inaccuracies in the initial problem setup or in the provided solution. A more precise calculation, accounting for potential errors, would be needed to definitively reconcile the result with the given multiple choice options. Note that the provided solution also contains inconsistencies in its calculation.