If any object is rotated, does it rotate with same angle with respect to any point on the object?

Question

Consider a 2D shape.
If it is rotated around any point $P$ on it, then $P$ is kept fixed.

Let there be another point $Q$ on it.
And compare the final position and initial axes at point $Q$.

Will the rotation with respect to $Q$ be the same as $P$?