Question

If a line, OA(O is origin) makes an angle of ${30}^{\circ }$ with the negative x-axis, the angle it makes with the positive direction of x-axis is .

• A. ${60}^{\circ }$
• B. $-{150}^{\circ }$
• C. ${120}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

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

The situation is:

We can measure the angles in two directions - clockwise(-) and anti-clockwise(+).

If we measure the angle in clockwise direction:


In the figure we can see that $\alpha$ and ${30}^{\circ }$ are supplementary angles.
$\Rightarrow \alpha ={150}^{\circ }$

$\alpha$ is the angle made by OA with with respect to +ve x-axis when we measure it in clockwise direction. Magnitude of that angle is ${150}^{\circ }$ and its sign is negative. So, the angle is $-{150}^{\circ }$.