Doua drepte concurente formeaza 4 unghiuri cu masuri egale doua cate doua: masurile unghiurilor opuse la varf.
Astfel ca:
[tex]m(\measuredangle A_1)=m(\measuredangle A_3)[/tex]
[tex]m(\measuredangle A_2)=m(\measuredangle A_4)[/tex]
Suma tuturor celor 4 unghiuri este de 360°, pentru ca atatea grade are o rotatie completa in jurul punctului de concurenta a dreptelor.
Mai mult decat atat, suma a 2 unghiuri consecutive (dintre cele 4) este de 180°.
Adica:
[tex]m(\measuredangle A_1)+m(\measuredangle A_2)=180^\circ[/tex]
[tex]m(\measuredangle A_3)+m(\measuredangle A_4)=180^\circ[/tex]
a. [tex]m(\measuredangle A_1)=25^\circ\implies m(\measuredangle A_3)=25^\circ[/tex]
[tex]m(\measuredangle A_2)=180^\circ-m(\measuredangle A_1)=180^\circ-25^\circ=155^\circ[/tex]
[tex]\implies m(\measuredangle A_4)=155^\circ[/tex]
b. [tex]m(\measuredangle A_1)=37^\circ43'\implies m(\measuredangle A_3)=37^\circ43'[/tex]
[tex]m(\measuredangle A_2)=180^\circ-37^\circ43'[/tex]
Stim ca [tex]1^\circ=60'[/tex]
Deci
[tex]m(\measuredangle A_2)=179^\circ-37^\circ+1^\circ-43'=142^\circ+60'-43'=142^\circ17'[/tex]
[tex]\implies m(\measuredangle A_4)=142^\circ17'[/tex]
c. [tex]m(\measuredangle A_1)=92^\circ13'\implies m(\measuredangle A_3)=92^\circ13'[/tex]
[tex]m(\measuredangle A_2)=180^\circ-92^\circ13'=179^\circ-92^\circ+60'-13'=87^\circ47'[/tex]
[tex]\implies m(\measuredangle A_4)=87^\circ47'[/tex]
