In parallelogram \(ABCD\), let \(E\) and \(F\) be the feet of the altitudes from \(A\) and \(B\) to \(DC\) and \(AD\), respectively. If \(\angle EAB = 35^\circ\) and \(\angle BCF = 45^\circ\), find the measure of \(\angle AEF\). Let's think step by step and output the final answer within \boxed{}.
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