Answer:
[tex]m\angle ADC=132^\circ[/tex]
Step-by-step explanation:
The Law of Sines
It is an equation relating the lengths of the sides of a triangle to the sines of its opposite angles. If A, B, and C are the lengths of the sides and a,b,c are their respective opposite angles, then:
[tex]\displaystyle \frac{A}{\sin a}=\frac{B}{\sin b}=\frac{C}{\sin c}[/tex]
We have completed the figure with the variable x for angle BDA. Thus
[tex]\displaystyle \frac{35}{\sin 120^\circ}=\frac{30}{\sin x}[/tex]
Solving for x:
[tex]\displaystyle \sin x=\frac{30\sin 120^\circ}{35}[/tex]
Calculating:
[tex]\sin x=0.742[/tex]
[tex]x=\arcsin 0.742[/tex]
[tex]x\approx 48^\circ[/tex]
Since angles ADC and x are linear, their sum is 180° and:
[tex]m\angle ADC=180^\circ-48^\circ[/tex]
[tex]\mathbf{m\angle ADC=132^\circ}[/tex]
