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Raportul masurilor a doua unghiuri suplimentare este 5/7.Calculati masurile acestora.Doua unghiuri complementare au masurile invers proportionale cu 2 si 3 .Calculati masurile celor doua unghiuri.

Răspuns :

a/b=5/7
a=5k
b=7k
a+b=180°
5k+7k=180°
12k=180°
k=180°:12
k=15°
a=5*15°=75°
b=7*15°=105°

a/1/2=b/1/3=k
a=1/2*k=k/2
b=1/3*k=k/3
a+b=90°
k/2+k/3=90°
3k/6+2k/6=90°
5k/6=90°
5k=90° *6
5k=540°
k=540°:5
k=108°
a=108°/2=54°
b=108°/3=36°
Alinsmarandach
∡A+∡B=180°
A\B=5/7⇒7A=5B⇒A=5B/7
5B/7+B=180°⇒5B/7+7B/7=180°⇒12B/7=180°⇒∡B=180*7/12=105°
∡A=180-105=75°

∡A*2=∡B*3  si ∡A+∡B=90°
A=3B/2⇒3B/2+B=90°⇒3B/2+2B/2=90°⇒5B/2=90°⇒∡B=90*2/5=36°
∡A=90-36=54°

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