Answer:
∠ A = 43°
Step-by-step explanation:
Since the triangles are similar then corresponding angles are congruent, so
∠ B = ∠ T = 55°
The sum of the 3 angles in a triangle = 180°
sum the 3 angles in Δ ABC and equate to 180
2x - 9 + 3x + 4 + 55 = 180 , that is
5x + 50 = 180 ( subtract 50 from both sides )
5x = 130 ( divide both sides by 5 )
x = 26
Then
∠ A = 2x - 9 = 2(26) - 9 = 52 - 9 = 43°
