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In the rectangle below, EI= 4x+7, FI = 5x+5, and mZFIG= 54º.Find EG and m ZIHE.EF1EG =15?m ZIHE =HGContinue2021 McGraw-Hill Education. All Rights ReserveSearch for anything

In the rectangle below EI 4x7 FI 5x5 and mZFIG 54ºFind EG and m ZIHEEF1EG 15m ZIHE HGContinue2021 McGrawHill Education All Rights ReserveSearch for anything class=

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SOLUTION

[tex]\begin{gathered} EI=4x+7 \\ EG=2(EI) \\ EG=2(4x+7) \\ EG=8x+14 \\ \\ FI=5x+5 \\ FH=2(FI) \\ FH=2(5x+5) \\ FH=10x+10 \end{gathered}[/tex]

To find x, equate both diagonals FH and EG as they are equal

[tex]\begin{gathered} FH=EG \\ 10x+10=8x+14 \\ 10x-8x=14-10 \\ 2x=4 \\ x=2 \end{gathered}[/tex]

To find EG

[tex]\begin{gathered} EG=8x+14 \\ =8(2)+14 \\ =16+14 \\ =30 \end{gathered}[/tex]

EG = 30

Since lenght IE and IH are equal (15) , triangle IHE is an iscoceless triangle

with equal base angles

x+x+54=180

2x+54=180

2x=180-54

2x=126

x=126/2

x=63degrees.

[tex]\begin{gathered} \text{Therefore} \\

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