Step 1: Find the slope of the first line. From $\sqrt{3}$x + y = 1, we get y = -$\sqrt{3}$x + 1. Therefore, slope m₁ = -$\sqrt{3}$.

Step 2: Find the slope of the second line. From x + $\sqrt{3}$y = 1, we get y = (-1/$\sqrt{3}$)x + 1/$\sqrt{3}$. Therefore, slope m₂ = -1/$\sqrt{3}$.

Step 3: Apply the formula for angle between two lines: tan θ = |(m₁ - m₂)/(1 + m₁m₂)|

Step 4: Calculate m₁ - m₂ = -$\sqrt{3}$ - (-1/$\sqrt{3}$) = -$\sqrt{3}$ + 1/$\sqrt{3}$ = -2/$\sqrt{3}$

Step 5: Calculate m₁m₂ = (-$\sqrt{3}$)(-1/$\sqrt{3}$) = 1, so 1 + m₁m₂ = 2

Step 6: Therefore, tan θ = |-2/$\sqrt{3}$ ÷ 2| = 1/$\sqrt{3}$

Step 7: Since tan θ = 1/$\sqrt{3}$, we get θ = 30°

Step 8: The angles between two intersecting lines are θ and (180° - θ), so the angles are 30° and 150°.