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Line LM is the midsegment of trapezoid ABCD. AB = x + 8, LM = 4x + 3, and DC = 187. What is the value of x? (image attached)thank you ! :)

Line LM Is The Midsegment Of Trapezoid ABCD AB X 8 LM 4x 3 And DC 187 What Is The Value Of X Image Attachedthank You class=

Answer :

To solve that question we must remember that

Then

[tex]\text{ LM = }\frac{\text{ AB + DC}}{2}[/tex]

Using the value the problem gives, we get the following equation

[tex]4x+3=\frac{(x+8)+187}{2}[/tex]

Solving that equation for x

[tex]\begin{gathered} 4x+3=\frac{(x+8)+187}{2} \\ \\ 8x+6=(x+8)+187 \\ \\ 7x=2+187 \\ \\ 7x=189 \\ \\ x=\frac{189}{7} \\ \\ x=27 \end{gathered}[/tex]

The value of x is 27.

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