Answer:
m∠ADC = 132°
Step-by-step explanation:
From the figure attached,
By applying sine rule in ΔABD,
[tex]\frac{\text{sin}(\angle ABD)}{\text{AD}}=\frac{\text{sin}(\angle ADB)}{AB}[/tex]
[tex]\frac{\text{sin}(120)}{35}=\frac{\text{sin}(\angle ADB)}{30}[/tex]
sin(∠ADB) = [tex]\frac{30\text{sin}(120)}{35}[/tex]
= 0.74231
m∠ADB = [tex]\text{sin}^{-1}(0.74231)[/tex]
= 47.92°
≈ 48°
m∠ADC + m∠ADB = 180° [Linear pair of angles]
m∠ADC + 48° = 180°
m∠ADC = 180° - 48°
m∠ADC = 132°
