Angle Chase!

Geometry Level 5

In \(\triangle ABC\), \(\angle A=70^\circ\), \(D\) is on the side \(AC\), and the angle bisector of \(\angle A\) intersects \(BD\) at \(H\) and \(BC\) at \(E\) such that \(AH:HE=3:1\) and \(BH:HD=5:3\). Then what is the measure of \(\angle C\) in degrees?

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