Respuesta :

answer:

y = 114°    and   x = 120°

step-by-step explanation:

part A:

  • one inner angle: 51°
  • second inner angle: (180°-87°) = 93°
  • third inner angle: (180°-30°) = 150°
  • fourth, beside y angle: 360° - 150° - 93° - 51° = 66°
  • then y = 180°  - 66°  = 114°

part B:

  • there are 6 sides, so inner angle: (6-2)*180 = 720°
  • 160° + 123° + 107° + 90° + x + x = 720°
  • 2x + 480° = 720°
  • 2x = 720° = 480°
  • 2x = 240°
  • x = 120°

#1

Let the angle beside y be x

[tex]\\ \rm\hookrightarrow x+51+(180-87)+(180-30)=360[/tex]

[tex]\\ \rm\hookrightarrow x+51+93+150=360[/tex]

[tex]\\ \rm\hookrightarrow x+294=360[/tex]

[tex]\\ \rm\hookrightarrow x=66[/tex]

  • y=180-66=114°

#2

[tex]\\ \rm\hookrightarrow 2x+123+107+160+90=720[/tex]

[tex]\\ \rm\hookrightarrow 2x+480=720[/tex]

[tex]\\ \rm\hookrightarrow 2x=240[/tex]

[tex]\\ \rm\hookrightarrow x=120[/tex]

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