Relax

Respuesta :

Answer:

See below ~

Step-by-step explanation:

Solving for x in ΔLMN

  • 6x + 3 + 4x - 10 + 5x + 7 = 180
  • 15x = 180
  • x = 12

Angles in ΔLMN

  • (6x + 3)° = 6(12) + 3 = 75°
  • (4x - 10)° = 4(12) - 10 = 38°
  • (5x + 7)° = 5(12) + 7 = 67°

Solving for y in ΔSTU

  • 5x + 3y + 9y - 7 + 6x - 5 = 180
  • 11x + 12y - 12 = 180
  • 11(12) + 12y = 192
  • 132 + 12y = 192
  • 12y = 60
  • y = 5

Angles in ΔSTU

  • (5x + 3y)° = 5(12) + 3(5) = 60 + 15 = 75°
  • (9y - 7)° = 9(5) - 7 = 45 - 7 = 38°
  • (6x - 5)° = 6(12) - 7 = 72 - 7 = 67°

⇒ Their angles are equal (in ΔLMN and ΔSTU)

⇒ ΔLMN and ΔSTU are similar

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