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The total sum of the angles must give 360 then:
[tex]\begin{gathered} 360=(8x-2)+90+(12x-8)+100 \\ 360=(8x+12x)+(100-2+90-8) \\ 360=20x+180 \\ 20x=360-180 \\ 20x=180 \\ x=\frac{180}{20} \\ x=9º \end{gathered}[/tex]