# Mysterious Angle Relation

Geometry Level 5

Let $$ABCD$$ be a trapezoid with $$AB\parallel DC$$ such that $$\angle DAC=50^{\circ}, \angle DBC=60^{\circ}$$. Suppose $$AC\cap DB=E$$, then denote $$G,F$$ the projections from $$E$$ onto $$AD,BC$$, $$M$$ is the midpoint of $$GF$$.

If $$O$$ is the circumcenter of $$\triangle DEC$$, find $$\angle MEO$$ in degrees.

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