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.
It is easy to find the magnitude of both the angles. θ2 and 30∘ are vertically opposite angles. So the magnitude of θ2 will be 30∘. θ1 and 30∘ when added will give us 180∘. So the magnitude of θ1 will be 150∘.
Now we have to find the sign of both the angles. θ2 is measured in clockwise direction. So the sign will be -ve. θ1 is measured anti-clockwise direction. So the sign will be +ve.
⇒θ1=150∘
θ2=30∘
⇒θ1+θ2=150∘−30∘
=120∘
(1) considering the sign of angles
(2) Concept of vertically opposite angles