Two regular pentagons $ ABCDE$ and $ AEKPL$ are placed in space so that $ \angle DAK=60^{\circ}$. Prove that the planes $ ACK$ and $ BAL$ are perpendicular.
Source: Ukraine 1997 grade 10
Tags: geometry proposed, geometry
Two regular pentagons $ ABCDE$ and $ AEKPL$ are placed in space so that $ \angle DAK=60^{\circ}$. Prove that the planes $ ACK$ and $ BAL$ are perpendicular.