# The bisector AL is drawn in triangle ABC, the angle ALC is 37 °, the angle ABC is 25 °. Find the angle of the ACB.

May 31, 2020 | Education

| Consider the triangle ABL.

∠BLA = 180 ° -∠ALC = 180 ° -37 ° = 143 ° (as these are adjacent angles)

By the theorem on the sum of the angles of a triangle:

180 ° = ∠ABC + ∠BLA + ∠LAB = 25 ° + 143 ° + ∠LAB

∠LAB = 180 ° -25 ° -143 ° = 12 °

Consider the triangle ALC.

∠LAC = ∠LAB = 12 ° (since AL is a bisector)

By the theorem on the sum of the angles of a triangle:

180 ° = ∠ALC + ∠ACB + ∠LAC = 37 ° + ∠ACB + 12 °

∠ACB = 180 ° -37 ° -12 ° = 131 °

Answer: 131

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