Let the angle made by the line OA with respect to positive x -axis be -1 and the angle made by O B be -2 - Find the value of -1-20 -1-2- - 180- - Angle measured in clockwise direction is negative and angle measured in anti-clockwise direction is positive-

It is easy to find the magnitude of both the angles. θ_2 and 30^∘ are vertically opposite angles. So the magnitude of θ_2 will be 30^∘. θ_1 and 30^∘ when added ...

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Standard XI

Mathematics

Allied Angles

Let the angle...

Question

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.

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Solution

It is easy to find the magnitude of both the angles. $θ_{2}$ and $30^{\circ}$ are vertically opposite angles. So the magnitude of $θ_{2}$ will be $30^{\circ}$ . $θ_{1}$ and $30^{\circ}$ when added will give us $180^{\circ}$ . So the magnitude of $θ_{1}$ will be $150^{\circ}$ .

Now we have to find the sign of both the angles. $θ_{2}$ is measured in clockwise direction. So the sign will be -ve. $θ_{1}$ is measured anti-clockwise direction. So the sign will be +ve.

$\Rightarrow θ_{1} = 150^{\circ}$

$θ_{2} = 30^{\circ}$

$\Rightarrow θ_{1} + θ_{2} = 150^{\circ} - 30^{\circ}$

$= 120^{\circ}$

(1) considering the sign of angles

(2) Concept of vertically opposite angles

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Let the angle made by the line OA with respect to positive x-axis be θ1 and the angle made by OB be θ2. Find the value of θ1+θ2(0≤|θ1|,|θ2|≤180∘). Angle measured in clockwise direction is negative and angle measured in anti-clockwise direction is positive. __