Distance is not perpendicular

Geometry Level 4

A straight line \(L\) passes through \((1,2)\) and intersects the line \(x+y=4\) at a distance \(\frac{\sqrt6}{3}\) from \((1,2).\)

Over all possible \(L\), what is the largest acute angle, in degrees, that the line \(L\) makes with the \(x\)-axis?

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