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Rus_ich [418]
3 years ago
14

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

Mathematics
1 answer:
umka21 [38]3 years ago
4 0

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°

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