Question: I have been looking for the answer to this question but I haven’t found anything related.
I will use the following image as an example.

![Image](https://i.stack.imgur.com/ubPBJ.jpg)

As you can see, there is a circle divided in different parts of the same size and their corresponding angle is indicated.
So what do I mean with “getting the opposite angle”?
Based on the image, let’s say I want to get the opposite angle of 60.
While searching I have found that there’s one way to get the opposite angle, but it’s not exactly what I need. Those answers said that to get it I should add 180 to 60, but the problem is that it gives me 240, and that’s not what I need.
I should get 120 as the value, the opposite horizontal angle.
Is there any way to get this?

Answer: 
It is the supplementary angle with a common sine value of the given angle.

$$ \sin x =\sin \alpha$$

$$ x\_1= \alpha, x\_2= 180^{\circ} -\alpha$$

It is not on the opposite side in the diagram you have given. It is mirrored with respect to y-axis.
You've got your concept wrong.. You don't add $180$ to $60$.. Take any angle say $x$. The opposite angle of $x$ when added with $x$ will always sum up to give 180.. So opposite angle of $x$ is equal to $(180-x)$..
Then what's gonna be the opposite angle of $60$?
Exactly.. $180-60$.. which is $120$
This is also known as the Linear pair property of angles.