Let \(O\) and \(H\) be the circumcenter and the orthocenter of a \(\triangle ABC\) respectively. The line passing through the midpoint of \(OH\) and parallel to \(BC\) meets \(AB\) and \(AC\) at points \(D\) and \(E\) respectively. It is known that \(O\) is the incenter of \(\triangle ADE\). Find the measure of \(\angle A\) in degree measures.

Source:- SGO Class 8..

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