The bisector AL is drawn in the triangle ABC, the angle ALC is 112∘, the angle ABC is 106∘. Find the ACB angle.

The angle at the apex of the triangle is known <ABC = 106 and <ALC = 112.
All calculations will be performed in degrees, since the data is given in degrees.
Let’s define the angle <BLA = 180 – <ALC = 180 – 112 = 68.
Since AL is a bisector, then <BAL = <BAC / 2 = 180 – <ABL – <BLA = 180 -106 – 68 = 6,
Hence, the angle <BAC = 2 * (<BAL) = 2 * 6 = 12
Let’s find the angle <ACB from triangle ABC: <ACB = 180 – <ABC – <BAC = 180 – 12 – 106 = 62.