In circle \( O \), two chords \( AB \) and \( CD \) intersect at point \( E \). If \( \angle AEC \) is \( 60^\circ \) and the measure of the intercepted arc \( \widehat{AB} \) is 140 degrees, find the measure of the intercepted arc \( \widehat{CD} \). Let's think step by step and output the final answer within \boxed{}.
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