Answer:
m∠ADC = 132°
Step-by-step explanation:
Use sine rule to find m<ADB
[tex] \frac{b}{sin(B)} = \frac{d}{sin(D)} [/tex]
b = AD = 35
B = m∠ABD = 120º
d = AB = 30
D = m∠ADB = ?
Plug in the values
[tex] \frac{35}{sin(120)} = \frac{30}{sin(D)} [/tex]
[tex] \frac{35}{sin(120)} = \frac{30}{sin(D)} [/tex]
Cross multiply
[tex] 35 \times sin(D) = 30 \times sin(120) [/tex]
Divide both sides by 35
[tex] \frac{35 \times sin(D)}{35} = \frac{30 \times sin(120)}{35} [/tex]
[tex] sin(D) = \frac{30 \times sin(120)}{35} [/tex]
[tex] sin(D) = 0.7423 [/tex]
[tex] D = sin^{-1}(0.7423) [/tex]
[tex] D = 48 [/tex] (nearest integer)
D = m∠ADB = 48°
m∠ADC = 180 - m∠ADB (angles on a straight line)
m∠ADC = 180 - 48° (substitution)
m∠ADC = 132°
