The missing angle x is calculated as: 50.41°
How to use Law of sines?
The law of sines states that:
a/sin A = b/sin B = c/sin C
Using law of sines, we can say that:
5.6/sin 78 = BD/sin 50
BD = (5.6 * sin 50)/sin 78
BD = 4.386 cm
Using the concept of Linear pairs:
∠BDC = 180 - 78
∠BDC = 102°
9.3/sin 102 = 4.386/sin C
sin C = (4.386 * sin 102)/9.3
sin C = 0.4613
C = sin⁻¹0.4613
C = 27.59°
B = 180 - (102 + 27.59)
B = 50.41°