ABCD parallelogram. AM is the bisector of angle A. M belongs to BC. The angle AMC is 138 degrees. Find the angles ABCD.

∠АМС and АМВ are adjacent. So ∠АМС + ∠АМВ = 180 °.
Find ∠АМВ = 180 ° – ∠АМС = 180 ° – 138 ° = 42 °.
By condition, AM is the bisector of ∠A. Consequently, it cuts off the EQUALIBLE ∆АВМ from the parallelogram.
In isosceles triangles, the angles at the base are equal. Those. ∠ВМ = ∠ВМА = 42 °.
Because the sum of the angles of a triangle is 180 °. Then we get: ∠ABM + ∠AMB + ∠BAM = 180 °.
We find the unknown ∠ABM = 180 ° – ∠AMB – ∠BAM = 180 ° – 42 ° – 42 ° = 96 °.
AM is a bisector. ∠А = ∠ВАМ + ∠ВМА = 42 ° + 42 ° = 84 °.
In a parallelogram, opposite angles are equal. This means that ∠A = ∠C = 84 ° and ∠B = ∠D = 96 °.
Answer: ∠А = ∠С = 84 ° and ∠В = ∠D = 96 °.