Find the acute angle between the lines $3 x + y - 7 = 0$ and $x + 2 y - 9 = 0.$

45^{o}

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135^{o}

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60^{o}

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120^{o}

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Solution

The correct option is A $45^{o}$
Angle between two lines $θ$ is given by
$θ = {t a n}^{- 1} ∣ ∣ ∣ \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} ∣ ∣ ∣$
where $m_{1} = - 3$ is the slope of one line.
$m_{2} = \frac{- 1}{2}$ is the slope of other line.
$tan θ = ∣ ∣ ∣ ∣ \frac{- 3 + \frac{1}{2}}{1 + \frac{3}{2}} ∣ ∣ ∣ ∣ = 1$
$\Rightarrow θ = 45^{0}$
Ans: A

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