In the adjoining figure, \( A B C D \) is a square, diagonal \( B D \) is extended through \( D ...

In the adjoining figure, \( A B C D \) is a square, diagonal \( B D \) is extended through \( D \) to E. \( A D=D E \) and \( A E \) is drawn as shown in figure. What is the measure of E \( \angle D A E ? \)