Question 98
The quadrilateral regular pyramid $VABCD$ has basis $ABCD$. The points $M$, $N$ and $P$ are the midpoints of the edges $AD$, $BC$, respectively $VA$. Prove that the angle of the line $CP$ with the plane $(BAD)$ has $45^\circ$ if and only if the angle of the line $CP$ with the plane $(VMN)$ has $30^\circ$.