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12. In the diagram below, transversal TU intersects PQ and RS at V and W, respectively. If mZTVQ = 5x - 22 and mZTVQ = 3x + 10, for which value of x is PQ parallel to RS? P_ R W A. 6 B. 16 C. 24 D. 28

12 In the diagram below transversal TU intersects PQ and RS at V and W respectively If mZTVQ 5x 22 and mZTVQ 3x 10 for which value of x is PQ parallel to RS P R class=

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ANSWER:

The value of x is 16

STEP-BY-STEP EXPLANATION:

With the information given, they tell us that TVQ can be expressed in two ways, but in the end the value must be the same because it is the same angle.

Thanks to this we can make the following equality:

[tex]5x-22=3x+10[/tex]

Solving for x:

[tex]\begin{gathered} 5x-3x=22+10 \\ 2x=32 \\ x=\frac{32}{2} \\ x=16 \end{gathered}[/tex]

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