1. The problem describes two coordinate systems sharing the same origin $O$, with axes $X, Y$ and rotated axes $X', Y'$. 2. The angle between the original $X$ axis and the rotated $X'$ axis is $\Theta$. 3. Points $M$ and $N$ lie on the $X$ axis, while $M'$ and $N'$ lie on the rotated $X'$ axis. 4. The point $P$ is defined vertically from $M$ (or $N$) forming perpendicular lines to the $X$ axis. 5. The angle $\Theta$ represents the amount of rotation of the $X'$ axis relative to the $X$ axis. 6. By construction, rotating the coordinate axes by an angle $\Theta$ means any point $P$ on $X'$ axis forms the angle $\Theta$ with respect to the original $X$ axis. 7. The angle $\Theta$ is measured counterclockwise from $X$ to $X'$, so the point $P$ on $X'$ is effectively the image of a rotation of the point on $X$ by $\Theta$. In summary, point $P$ shows angle $\Theta$ because the $X'$ axis is rotated by $\Theta$ relative to the original $X$ axis, so any point on $X'$ appears at an angle $\Theta$ in the original coordinate system.