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

B
D
30
35
A
С
In the figure, if m_ABD = 120°, then m_ADC =
-4345

Type the correct answer in the box. Round your answer to the nearest integer. B D-example-1

1 Answer

3 votes

Answer:


m\angle ADC=132^\circ

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 (A)/(\sin a)=(B)/(\sin b)=(C)/(\sin c)

We have completed the figure with the variable x for angle BDA. Thus


\displaystyle (35)/(\sin 120^\circ)=(30)/(\sin x)

Solving for x:


\displaystyle \sin x=(30\sin 120^\circ)/(35)

Calculating:


\sin x=0.742


x=\arcsin 0.742


x\approx 48^\circ

Since angles ADC and x are linear, their sum is 180° and:


m\angle ADC=180^\circ-48^\circ


\mathbf{m\angle ADC=132^\circ}

Type the correct answer in the box. Round your answer to the nearest integer. B D-example-1
User Usman Ghauri
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