Respuesta :

semsee45

Answer:

x = 10

m∠K = 90°

y = 15

JM = 65

Step-by-step explanation:

KJ = LM

⇒ x + 31 = 5x - 9

⇒ 40 = 4x

⇒ x = 10

From inspection of the diagram, m∠K = 90° (right angle)

KL = JM

⇒ 4y + 5 = 2y + 35

⇒ 2y = 30

⇒ y = 15

JM = 2y + 35

⇒ JM = 2(15) + 35

⇒ JM = 30 + 35

⇒ JM = 65

Opposite sides of rectangle are equal

[tex]\\ \rm\Rrightarrow x+31=5x-9[/tex]

[tex]\\ \rm\Rrightarrow 4x=40[/tex]

[tex]\\ \rm\Rrightarrow x=10[/tex]

  • m<K=90°

[tex]\\ \rm\Rrightarrow 4y+5=2y+35[/tex]

[tex]\\ \rm\Rrightarrow 2y=30[/tex]

[tex]\\ \rm\Rrightarrow y=15[/tex]

  • KL=JM=2(15)+35=30+35=65

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