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 $45^{\circ}$. 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 1.
Answer: 1) $75^{0}, 105^{0}$; 2) $S_{\text {ABCD }}=\frac{\sqrt{3}+1}{4}$.