Răspuns:
Explicație pas cu pas:
a.fie a,b,c,d cele 4 unghiuri, daca sunt invers proporționale <=> a*4 = b * 5 = c * 8 = d*40 = k => a = k/4, b = k/5, c = k/8 si d=k/40
a+b+c+d = 360° <=> k/4+k/5+k/8+k/40 = 360 => 10k+8k+5k+1 = 40*360 =>
24k = 40*360 , deci k = 40*360/24 = 5*120=600°
a = 600/4=150
b = 600/5=120
c = 600/8=75
d = 600/40=15
b. se procedeaza la fel si vom avea ca :
a = k/3, b = k/4, c = k/6 si d=k/12
k/3+k/4+k/6+k/12 = 360
4k+3k+2k+k=12*360
10k=12*360 => k=12*36=432
a = 432/3=144
b = 432/4=108
c = 432/6=72
d= 432/12=36
