Question

What is the angle between the two straight lines $y = (2 - \sqrt{3})x + 5$ and $y = (2 + \sqrt{3}) x - 7$?

• A. $60^{\circ}$
• B. $45^{\circ}$
• C. $30^{\circ}$
• D. $15^{\circ}$

Answer 1

Answer: (A)

The given lines are
$y = (2 - \sqrt{3}) x + 5$
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+\left(4-3\right)}\right| $
$= \left|\frac{2\sqrt{3}}{2}\right| = \sqrt{3} = \tan \frac{\pi}{3} \Rightarrow \theta = \frac{\pi}{3} = 60^{\circ} $