Question

In the rectangle below, BD= 4x - 2, AC = 5x-11, and m ZAED=82º.Find AE and m ZECB.BEAE =01mZECB =DA

Answer 1

Given data:

The given figure of the rectangle.

The length of diagonal are equal.

`\begin{gathered} BD=AC \\ 4x-2=5x-11 \\ 4x-5x=-11+2 \\ -x=-9 \\ x=9 \end{gathered}`

The lenght AE is,

`\begin{gathered} AE=(AC)/(2) \\ =(5(9)-11)/(2) \\ =17 \end{gathered}`

The triangle BEC is an isosceles triangle,

`\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}`

Thus, the lenght of the side AE is 17, and the angle ECB is 49 degrees.