The line OA makes an angle of $θ = 40 °$ with the negative X-axis as shown in the figure. Which of the following could be a measure of the angle made by OA with respect to the positive Y-axis?

+50˚

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+130˚

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-230˚

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-130˚

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Solution

The correct option is C
-230˚
We can measure the angle made by OA with the positive Y-axis in two directions, anticlockwise ( $φ$ ) or clockwise ( $ϕ$ ).
For measuring angle in anticlockwise direction, we see
$φ = (90 ˚ + θ) = (90 ˚ + 40 ˚) = + 130 ˚$
Also, in clockwise direction,
angle made $ϕ = - (180 ˚ + (90 ˚ - 40 ˚)) = - (180 ˚ + 50 ˚) = - 230 ˚$
$So, measuring the angle subtended in clockwise direction, we get angle ϕ = - 230 ° . and, Measuring the angle subtended in anticlockwise direction, we get angle φ = + 130 ° .$

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The line OA makes an angle of θ=40° with the negative X-axis as shown in the figure. Which of the following could be a measure of the angle made by OA with respect to the positive Y-axis?

The line OA makes an angle of $θ = 40 °$ with the negative X-axis as shown in the figure. Which of the following could be a measure of the angle made by OA with respect to the positive Y-axis?