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In the image below ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯∥⎯⎯⎯⎯⎯⎯⎯⎯⎯LM¯∥OP¯. Given the lines are parallel, ∠≅∠∠LMN≅∠PON because and that ∠≅∠∠LNM≅∠ONP by the , you can conclude the triangles are similar by the AA Similarity Theorem. If NP = 20, MN = x+ 6, NO = 15, and LN = 2x - 3 then x = .

In the image below LMOP Given the lines are parallel LMNPON because and that LNMONP by the you can conclude the triangles are similar by the AA Similarity Theor class=

Respuesta :

Given:

Required:

We need to answer the questions

Explanation:

Angle LMN and angle PON are the congruent because both are alternate angles

Now angle LNM and angle ONP are also congruent because those two triamgles are similar and both are internal angles

Now to find the value of x

[tex]\begin{gathered} \frac{NP}{MN}=\frac{NO}{LN} \\ \\ \frac{20}{x+6}=\frac{15}{2x-3} \\ \\ 40x-60=15x+90 \\ 25x=150 \\ x=6 \end{gathered}[/tex]

Final answer:

x=6

Ver imagen PurposeN145851