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

In The Rectangle Below B D 4x 2 AC 5x11 And M ZAED 82ºFind AE And M ZECBBEAE M ZECB DС class=

Sagot :

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]

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