Fie o centrul unui cerc si doua unghiuri la centru adiacente aob si boc. stiind ca masura unghiului aob = 120 si masura boc= 150,aflati masurile unghiurilor triunghiului abc.

Let A be the center of a circle and two angles at the adjacent center AOB and BOC. Knowing the measure of the angle AOB = 120 and the measure BOC = 150, find the measures of the angles of the ABC triangle.
solution

Given the above information;
AC=AB, therefore ABC is an isosceles triangle. 
therefore, BAO=ABO=(180-120)/2=30
OAC=OCA=(180-90)/2=45
OBC=BCO=(180-150)/2=15
THUS;
BAC=BAO+OAC=45+30=75
ABC=OBA+CBO=15+30=45
ACB=ACO+BCO=15+45=60