Mathematics - Straight Lines Question with Solution | TestHub

The given lines are:
$y=(2-\sqrt{3})x+5\text{ and }y=(2+\sqrt{3})x-7$
Therefore, slope of first line $=m_1=2-\sqrt{3}$ and slope of second line $=m_2=2+\sqrt{3}$
$\therefore \tan \theta =\left|\frac{m_2-m_1}{1+m_1{m}_2}\right|=\left|\frac{2+\sqrt{3}-2+\sqrt{3}}{1+(4-3)}\right|$
$=\left|\frac{2\sqrt{3}}{2}\right|=\sqrt{3}=\tan \frac{\pi }{3}\Rightarrow \theta =\frac{\pi }{3}=60^{\circ }$