Respuesta :

Answer:

The value of x = 7

Step-by-step explanation:

Given the right triangle

  • Right angle = 90°
  • α = (4x+7)°
  • β =  (8x-1)°

  • We know that the sum of angles of a triangle is 180°.

so

Right angle + α + β =  180°

90° + 4x+7 + 8x-1 = 180

Group like terms

[tex]4x+8x+90+7-1=180[/tex]

Add similar elements: :4x+8x=12x

[tex]12x+90+7-1=180[/tex]

[tex]12x+96=180[/tex]

[tex]12x=84[/tex]

Divide both sides by 12

[tex]\frac{12x}{12}=\frac{84}{12}[/tex]

[tex]x = 7[/tex]

Therefore, the value of x = 7

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