Question

In the rectangle below, B D = 4x – 2, AC = 5x-11, and m ZAED = 82º.Find AE and m ZECB.BEAE =m ZECB =DС

Answer 1

Given :

$\begin{gathered} BD\text{ = 4x + 2} \\ AC\text{ = 5x - 11} \\ \angle AED=82^0 \end{gathered}$

Required :

$AE\text{ , }\angle\text{ ECB}$

Recall from the properties of a rectangle that

$\text{The diagonals have the same length}$

Hence :

$\begin{gathered} AC\text{ = BD} \\ 5x\text{ - 11 = 4x -2 } \\ \text{collect like terms} \\ 5x\text{ - 4x = 11 - 2} \\ x\text{ = 9} \end{gathered}$