Given a triangle ABC. We marked a point O such that AO = BO = CO. The angles AOB, BOC and COA are 44, 64, 108.

Given a triangle ABC. We marked a point O such that AO = BO = CO. The angles AOB, BOC and COA are 44, 64, 108. How many degrees is the greatest angle of triangle ABC?

1) The AOS triangle is isosceles, because AO = OS
Angle OSA = OSA = (180-108) / 2 = 36 (deg.)
2) Triangle AOB isosceles, OAB = OBA = (180-44) / 2 = 68 (deg.)
3) The triangle VOS is isosceles, OVS = OSV = (180-64) / 2 = 58 (deg.)
4) Angle BAC = BAO + OAC = 68 + 36 = 104 (deg.)
ABC = ABO + OBC = 68 + 58 = 126 (deg.)
BCA = BCO + OCA = 58 + 36 = 94 (deg.)
Answer: 126 degrees.