Given :
[tex]\begin{gathered} BD\text{ = 4x + 2} \\ AC\text{ = 5x - 11} \\ \angle AED=82^0 \end{gathered}[/tex]
Required :
[tex]AE\text{ , }\angle\text{ ECB}[/tex]
Recall from the properties of a rectangle that
[tex]\text{The diagonals have the same length}[/tex]
Hence :
[tex]\begin{gathered} AC\text{ = BD} \\ 5x\text{ - 11 = 4x -2 } \\ \text{collect like terms} \\ 5x\text{ - 4x = 11 - 2} \\ x\text{ = 9} \end{gathered}[/tex]
