Question

Type the correct answer in the box. Round your answer to the nearest integer.

Answer 1

Answer:

m∠ADC = 132°

Step-by-step explanation:

From the figure attached,

By applying sine rule in ΔABD,

$\frac{\text{sin}(\angle ABD)}{\text{AD}}=\frac{\text{sin}(\angle ADB)}{AB}$

$\frac{\text{sin}(120)}{35}=\frac{\text{sin}(\angle ADB)}{30}$

sin(∠ADB) = $\frac{30\text{sin}(120)}{35}$

                 = 0.74231

m∠ADB = $\text{sin}^{-1}(0.74231)$

             = 47.92°

             ≈ 48°

m∠ADC + m∠ADB = 180° [Linear pair of angles]

m∠ADC + 48° = 180°

m∠ADC = 180° - 48°

m∠ADC = 132°