If a line is making an angle of $30^{\circ}$ measured in anti-clockwise direction with the horizontal, what will be the angle formed by its image in a vertical line measured in anti-clockwise direction with the horizontal?

$30^{\circ}$

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$150^{\circ}$

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$120^{\circ}$

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$60^{\circ}$

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Solution

The correct option is B
$150^{\circ}$

If a line is making an angle of $30^{\circ}$ measured in anti-clockwise direction with the horizontal, then its reflection will also make an angle of $30^{\circ}$ with the horizontal but meadured in clockwise direction as shown in the figure:

We have to find the angle made by $O B$ with the horizontal measured in anti-clockwise direction.

$= 180 - 30 = 150^{\circ}$ [Linear Pair]

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Q. Angle measured in clockwise direction is positive and angle measured in anti-clockwise direction is negative

Q. Find the slope of the line which makes an angle of

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axis measured anti-clockwise.

Let the angle made by the line OA with respect to positive x-axis be $θ_{1}$ and the angle made by OB be $θ_{2}$ . Find the value of $θ_{1} + θ_{2} (0 \leq | θ_{1} |, | θ_{2} | \leq 180^{\circ})$ . Angle measured in clockwise direction is negative and angle measured in anti-clockwise direction is positive.