Question

The tangent of angle between the straight lines $x-y+5=0$ and $x+2y=0$ is

Answer 1

Slope of $x-y+5=0$ is $1$
Slope of $x+2y=0$ is $-\frac{1}{2}$
$m_1=1.$ $m_2=-\frac{1}{2}$
Angle between lines
$\tan \theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|=\left|\frac{1+\frac{1}{2}}{1+\left(\frac{-1}{2}\right)}\right|=3$
$\Rightarrow \tan \theta =3$