![m\angle ADC=132^\circ](/tpl/images/0949/5955/6e232.png)
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:
![\displaystyle \frac{A}{\sin a}=\frac{B}{\sin b}=\frac{C}{\sin c}](/tpl/images/0949/5955/c4c15.png)
We have completed the figure with the variable x for angle BDA. Thus
![\displaystyle \frac{35}{\sin 120^\circ}=\frac{30}{\sin x}](/tpl/images/0949/5955/f8cbf.png)
Solving for x:
![\displaystyle \sin x=\frac{30\sin 120^\circ}{35}](/tpl/images/0949/5955/e70c2.png)
Calculating:
![\sin x=0.742](/tpl/images/0949/5955/770fb.png)
![x=\arcsin 0.742](/tpl/images/0949/5955/9aad2.png)
![x\approx 48^\circ](/tpl/images/0949/5955/2d068.png)
Since angles ADC and x are linear, their sum is 180° and:
![m\angle ADC=180^\circ-48^\circ](/tpl/images/0949/5955/e832f.png)
![\mathbf{m\angle ADC=132^\circ}](/tpl/images/0949/5955/cca02.png)
![Type the correct answer in the box. Round your answer to the nearest integer.
B
D
30
35
A
С
In the](/tpl/images/0949/5955/d95bd.jpg)