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Given that \(\overline{AE} \bigcap \overline{BD} = \{ C \} \), and \(\overline{AF} \) bisects \(\angle DAE\), \(\vec {BF} \) bisects \(\angle DBE \), \(\angle AFB = 50^\circ \), find the measure of \( \angle ADB + \angle AEB \) in degrees.

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