In the pyramid $A B C D$, the angle $A B C$ is equal to $\alpha$, the orthogonal projection of point $D$ onto the plane $A B C$ is point $B$. Find the angle between the planes $A B D$ and $C B D$.
Since the orthogonal projection of point $D$ onto plane $A B C$ is point $B$, line $B D$ is perpendicular to plane $A B C$, so $A B \perp B D$ and $B C \perp B D$. Therefore, $A B C$ is the linear angle of the dihedral angle with faces $A B D$ and $C B D$. Consequently, the angle between planes $A B D$ and $C B D$ is $\alpha$.

Answer

## $\alpha$.