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Raportul masurilor a 2 unghiuri suplementare este 100 supra 50 . Aflati unghiurile.

Răspuns :

Fie A,B doua unghiuri
∡A+∡B=180°
[tex] \frac{A}{B} [/tex]=[tex] \frac{100}{50} [/tex]
50A=100B
=>A=[tex] \frac{100B}{50} [/tex]
[tex] \frac{100B}{50} [/tex]+B=180°
100B+50B=9000
150B=9000
=>B=60°
A=180°-60°
A=120°
[tex]\frac{m(\angle A)}{m(\angle B)} = \frac{100}{50} = 2\implies m(\angle A)=2m(\angle B)[/tex]
[tex]m(\angle A)+m(\angle B) = 180^o[/tex]
[tex]2m(\angle B)+m(\angle B)=180^o\implies m(\angle B) = 180^o:3 = 60^o[/tex]
[tex]m(\angle A) = 180^o-m(\angle B) = 180^o-60^o=120^o[/tex]