Answer:
x = 50.5°
Step-by-step explanation:
∠ BDC and ∠ BDA are adjacent and supplementary, thus
∠ BDC = 180° - 78° = 102°
Calculate ∠ BCD using the Sine rule in Δ ABC, that is
[tex]\frac{5.6}{sinC}[/tex] = [tex]\frac{9.3}{sin50}[/tex] ( cross- multiply )
9.3 × sinC = 5.6 × sin50° ( divide both sides by 9.3 )
sinC = [tex]\frac{5.6sin50}{9.3}[/tex] ≈ 0.4613, thus
C = [tex]sin^{-1}[/tex] (0.4613 ) ≈ 27.5°
The sum of the 3 angles in Δ BCD = 180°, thus
x = 180° - (102 + 27.5)° = 180° - 129.5° = 50.5°
