If ∠ BDC = x + 2 / 3 ∠ a, find the degree of X?

Let ∠ abd = β, ∠ ACD = γ
The BCD forms a triangle
Then, DBC + DCB + BDC = 180 degree
Then 2 β + 2 γ + α + 2 / 3 ∠ a = 180 ° (1)
Because ∠ DBC = 2 ∠ abd, ∠ DCB = 2 ∠ ACD
Then ∠ ABC = 3 β, ∠ ACB = 3 γ
From ∠ ABC + ∠ ACB + ∠ a = 180 degree
Then 3 β + 3 γ + a = 180 degree
Then 2 β + 2 γ + 2 / 3 ∠ a = 120 ° (2)
LIANLI (1) (2) available
α=60°

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