Given data:
The given figure of the rectangle.
The length of diagonal are equal.
[tex]\begin{gathered} BD=AC \\ 4x-2=5x-11 \\ 4x-5x=-11+2 \\ -x=-9 \\ x=9 \end{gathered}[/tex]
The lenght AE is,
[tex]\begin{gathered} AE=\frac{AC}{2} \\ =\frac{5(9)-11}{2} \\ =17 \end{gathered}[/tex]
The triangle BEC is an isosceles triangle,
[tex]\begin{gathered} \angle\text{AED}=\angle BEC=82^{\circ} \\ \angle EBC=\angle ECB \\ \angle BEC+\angle EBC+\angle ECB=180^{\circ} \\ 82^{\circ}+2\angle ECB=180^{\circ} \\ \angle ECB=49^{\circ} \end{gathered}[/tex]
Thus, the lenght of the side AE is 17, and the angle ECB is 49 degrees.
