6. Point $M$ is the midpoint of side $A D$ of parallelogram $A B C D$. Line $C M$ is inclined to the base $A D$ at an angle of $75^{\circ}$. Vertex $B$ is equidistant from line $C M$ and vertex $A$. Find the angles of the parallelogram. Find the area of the parallelogram if the length of the base $A D$ is 4.
Answer: 1) $75^{\circ}, 105^{\circ} ; 2) S_{A B C D}=4(\sqrt{3}+2)$.

## Final round of the "Rosatom" olympiad, 11th grade, Moscow, March 2020

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