You have that the triangle ACD is a reflection of triangle ABC arounf line AC. This means that line AD is a relfection of line AB, and line CD is a relflection of line BC.
If AD is reflection of AB, then AD has the same length as AB, hence:
AD = AB = 2.7
if CD is reflection of BC, then:
CD = BC = 3.2
Now, due to triangle ACD is reflection of ABC, angle ∠ACD (up right side) must be equal to ∠ABC (left down side), then:
∠ACD = ∠ABC = 64.3°
Furthermore, you can notice that angle ∠BAD is equal to angle ∠BCD. And the sum of all angles inside the figure must be equal to 360° (because it is a figure of four sides). Hence, you have:
∠BAD = ∠BCD
∠BAD + ∠BDC + 64.3° + 64.3° = 360°
∠BAD + ∠BAD + 64.3° + 64.3° = 360°
2∠BAD + 64.3° + 64.3° = 360°
2∠BAD + 128.6° = 360°
2∠BAD = 360° - 128.6°
2∠BAD = 231.4°
∠BAD = 231.4°/2
∠BAD = 115.7°
Hence, angle ∠BAD = ∠BCD is equal to 115.7°
