Why do we get angle $\theta$ between planes by taking dot product of the normal vectors?

Question

Let $\theta$ be the angle between 2 planes. Then to find this angle we take the dot product of the two normal vectors to the plane, divide by their magnitudes and then finally take the $\arccos$ of the resulting value.

However, after doing this why do we not get $180 - \theta$ and rather get $\theta$ ? angle between two planes

Answer 1

You will get theta as the answer if you are taking the smaller angle that is the angle between 0 and 90 as you know that cos is negative in the second quadrant hence we take modulus in these cases