Suma masurilor unghiurilor unui patrulater convax este de 360°
m(A)+m(B)+m(C)+m(D)=360°
m(A)+m(C)=190°
m(A)+m(B)+m(D)=280°
m(A)+m(C)+m(A)+m(B)+m(D)=280°+190°
2×m(A)+m(B)+m(C)+m(D)=470°
[2×m(A)+m(B)+m(C)+m(D)]-
[m(A)+m(B)+m(C)+m(D)]=470°-360°
m(A)=110°
m(C)=190°-110°=80°
m(B)-m(D)=30° =>m(B)=30°+m(D)
m(B)+m(D)=280°-m(A)
m(B)+m(D)=280°-110°
m(B)+m(D)=170°
30°+m(D)+m(D)=170°
2×m(D)=170°-30°
m(D)=140°:2
m(D)=70°
m(B)=30°+70°=100°
Raspuns:
m(A)=110°
m(B)=100°
m(C)=80°
m(D)=70°
m(A)+m(B)+m(C)+m(D)=
110°+100°+80°+70°=210°+150°=360°
