[ Linear dependence of vectors $]$ [ Angles between lines and planes $]$

The height of a regular hexagonal pyramid is equal to the side of the base. Find the angle between a lateral edge and the plane of the base.
Let ABCDEFP be a given regular hexagonal pyramid with vertex $P$; $M$ - the center of the regular hexagon $A B C D E F$. Denote $A B=B C=C D=D E=E F=A F=a$. Since the pyramid is regular, $P M$ is its height. Therefore, the angle of the lateral edge with the base plane is the angle $\angle PAM$. In the right triangle $A P M$, it is known that $P M=A M=a$, so $\angle P A M=45^{\circ}$.

## Answer

$45^{\circ}$.