The given lines are \(\sqrt3x+y=1\) and \(x+\sqrt3y=1.\)
\(y = -\sqrt3x + 1 … (1)\) and \(y = \frac{-1}{\sqrt3x} +\frac{ 1}{\sqrt3} …. (2)\)
The slope of line (1) is \(m_1 = -\sqrt3\) , while the slope of line (2) is \(m_2 =\frac{ -1}{\sqrt3}\)
The acute angle i.e., \(θ\) between the two lines is given by
\(Tanθ=\left|\frac{m_1-m_2}{1+m_1m_2}\right|\)
\(Tanθ=\left|\frac{-\sqrt3+\frac{1}{\sqrt3}}{1+(-\sqrt3)(\frac{-1}{\sqrt3})}\right|\)
\(Tanθ=\left|\frac{\frac{-3+1}{\sqrt3}}{1+1}\right|\)
\(=\left|\frac{-2}{2\times\sqrt3}\right|\)
\(Tanθ=\frac{1}{\sqrt3}\)
\(θ=30º\)
Thus, the angle between the given lines is either \( 30° \)or \(180° - 30° = 150°\).