Question

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

B
D
30
35
А
с
In the figure, if m ZABD = 120°, then mZADC =
0.

Answer 1

m∠ADC = 132°

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°