The bisector AL is drawn in the triangle ABC, the angle ALC is 128 degrees, the angle ABC is 109

The bisector AL is drawn in the triangle ABC, the angle ALC is 128 degrees, the angle ABC is 109 degrees. Find the angle ACB.

The sums of the angles of triangles ABC and ALC:

<BAC + <ABC + <BCA = 180 °;

<BAC = 180 ° – <ABC – <ACB = 180 ° – 109 ° – <ACB = 71 ° – <ACB;

<LAC + <ALC + <LCA = 180 °;

<LAC = 180 ° – <ALC – <ACL = 180 ° – 128 ° – <ACL = 52 ° – <ACB;

<BAC = 2 * <LAC (angle BAC divides the bisector);

71 ° – <ACB = 2 * (52 ° – <ACB);

71 ° – <ACB = 104 ° – 2 * <ACB;

Answer: <ACB = 33 °.