Respuesta :

Answer:

x = 7 , y = 37

Step-by-step explanation:

For Δ LMN ≅ Δ PQR

Then corresponding angles must be congruent, that is

∠ P = ∠ L , substitute values

9x - 18 = 5x + 10 ( subtract 5x from both sides )

4x - 18 = 10 ( add 18 to both sides )

4x = 28 ( divide both sides by 4 )

x = 7

Then

∠ P = 9x - 18 = 9(7) - 18 = 63 - 18 = 45°

∠ R = 180° - (84 + 45)° ← sum of angles in a triangle = 180°

∠ R = 180° - 129° = 51°

Then ∠ N = ∠ R

2x + y = 51

2(7) + y = 51

14 + y = 51 ( subtract 14 from both sides )

y = 37

aa010002

Answer:

[tex]x=7[/tex]

[tex]y=37[/tex]

Step-by-step explanation:

So if the angle of [tex]Q=M[/tex] we can assume that [tex]P=L[/tex] and [tex]N=R[/tex]. Since we don't have the equation for [tex]R[/tex] let's start with [tex]P[/tex] and [tex]L[/tex].

If [tex]P=L[/tex] that means that [tex](5x+10)=(9x-18)[/tex] from there we can subtract [tex]5x[/tex] which makes it so that [tex](10)=(4x-18)[/tex] from there we can add 18 to each side so we have [tex]28=4x[/tex] from there we simply divide both sides by 4 which gives us [tex]x=7[/tex]° we can then check that this is correct by doing [tex]5*7+10[/tex] which gives us 45° for [tex]L[/tex] and then [tex]9*7-18[/tex] which gives us 45° for [tex]P[/tex]

Since we know that the sum of the interior angles of all triangles has to be 180° that means that we can figure out the angle of [tex]N[/tex] and [tex]R[/tex] by doing [tex]180-(84+45)[/tex] which is 51. Assuming that [tex]N=51[/tex]° we can write something like [tex](2)(7)+y=51[/tex] which can be simplified into [tex]14+y=51[/tex], then you remove the 14 by subtracting it from both sides which leaves [tex]y=37[/tex]. Once again we have to double-check so [tex](2)(7)+37=N[/tex] and [tex]2*7=14[/tex] so [tex]14+37[/tex] obviously equals 51.

I hope this helped. If it did, feel free to mark my answer as brainliest! :)

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