This is only applicable when θ is less than 60.
Let x be the length of one side of the angle on the x-axis (Or whatever axis)
The angle formed with the pt. O and a pt on a circle with radius = x*(60/θ) and a circle of radius x with centre at B, Will be θ.

So could anyone help me with how this is it true (if it is at all.) and is there anything like this?
Actually I accidentally came to the above-mentioned conclusion this when I was trying to draw 20° without a protractor.