# The bisector AL is drawn in the triangle ABC, the angle ALC is 148 °, the angle ABC is 132 °. Find the angle of the ACB.

May 31, 2020 | Education

| Let ∠BAL = x

Then, ∠LAC also = x (since AL is a bisector).

Consider the triangle ABC:

∠ABC + ∠ACB + ∠CAB = 180 ° (by the theorem on the sum of the angles of a triangle).

132 ° + ∠ACB + 2x = 180 °

∠ACB + 2x = 48 °

x = (48 ° -∠ACB) / 2

Consider the triangle ALC:

∠ALC + ∠ACB + ∠LAC = 180 ° (by the theorem on the sum of the angles of a triangle).

148 ° + ∠ACB + x = 180 °

∠ACB + x = 32 °

Substitute the x value obtained earlier:

∠ACB + (48 ° -∠ACB) / 2 = 32 ° | * 2

2∠ACB + 48 ° -∠ACB = 64 °

∠ACB = 64 ° -48 ° = 16 °

Answer: 16

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