Question

The line OA makes an angle of $\theta ={30}^o$ with negative x-axis as shown in the figure. Which of the following could be the measure of the angle made by OA with respect to positive x-axis?

• A. $-{30}^o$
• B. $-{150}^o$
• C. ${210}^o$
• D. ${150}^o$

Answer 1

Answer: (B), (C)

${210}^o$

We can measure the angle in two directions; clockwise (-ve) and anti-clockwise (+ve). From the figure we can see that $\alpha$ and ${30}^o$ are supplementary angles.

$\Rightarrow ={150}^o$

$\alpha$ 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 ${150}^o$ and its sign is negative. So the angle is $-{150}^o$.

When we measure the angle in anti-clockwise direction, we get $\beta$.

$\beta ={180}^o+{30}^o$ (from the figure).

$\Rightarrow -{150}^{o}and{210}^o$ are the angles.

Key steps: (1) knowledge of sign convention while measuring the angles.

(2) Concept of supplementary angles.

(3) Same angle can be measured in different ways.