Răspuns:
<Ao=n°
<A1=(n+1)°
<A2=(n+2)°
-----------------_--------
<Am=n+m)°
Ao+A1+A2+...+Am=180°
n+(n+1)+(n+2)+...+(n+m)=180°
Ai m paranteze
n+n+1+n+2+...+n+m=180°
n(m+1)+m(m+1)/2=180°
2n(m+1)+m(m+1)=2*180
(m+1)(2n+m)=360°
(m+1)(m+2n=2³·3²·5
Observi ca m+1 si m+2n au paritati diferite
daca m+1numar impar m=numar par=>m=2n numar par ca suma de 2 numere pare
Caz1 m+1=nr impar=> m+1=9 =>m=8
Daca m=1=9=> m+2n=0 8+2n=40 => n=16
STA inseamna ca unghiurile pot fi
Ao=16;A1=17°;A2=18°,A3=19....A8=16+8=24
Explicație pas cu pas:
