Find the acute angle between lines having slopes 3 and −2.

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Answer

Let $m_1=3$ and $m_2=-2$.
Let $\theta$ be the acute angle between them.
$
\begin{aligned}
& \therefore \tan \theta=\left|\frac{m_1-m_2}{1+m_1 m_2}\right|=\left|\frac{3-(-2)}{1+(3)(-2)}\right|=\left|\frac{5}{-5}\right|=1 \\
& \therefore \quad \theta=45^{\circ}
\end{aligned}
$
The acute angle between lines having slopes 3 and -2 is $45^{\circ}$.

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