RO-NMO 2007 Problem 73

Consider the triangle $ABC$ with $m(\angle BAC) = 90^\circ$ and $AB < AC$ .Let a point $D$ on the side $AC$ such that: $m(\angle ACB) = m(\angle DBA)$ .Let $E$ be a point on the side $BC$ such that $DE\perp BC$ .It is known that $BD + DE = AC$ . Find the measures of the angles in the triangle $ABC$ .