Question

In the figure, if m∠ABD = 120º, then m∠ADC = ___

Answer 1

Answer-

$\boxed{\boxed{m\angle ADC=132^{\circ}}}$

Solution-

Law of Sines-

$\dfrac{a}{\sin A} =\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$

Here,

B = 120°

b = 35 units

d = 30 units

Let us assume that m∠ADC be x, so m∠ADB=180-x (as they are complementary angles)

Applying Laws of sine for ΔABD,

$\Rightarrow \dfrac{b}{\sin B}=\dfrac{d}{\sin D}$

$\Rightarrow \dfrac{35}{\sin 120}=\dfrac{30}{\sin (180-x)}$

$\Rightarrow \sin (180-x)=\dfrac{30\times \sin 120}{35}$

$\Rightarrow \sin (180-x)=\dfrac{3\sqrt{3}}{7}=0.742$

$\Rightarrow 180-x=\sin^{-1}0.742$

$\Rightarrow 180-x=47.9\approx 48$

$\Rightarrow x=180-48=132^{\circ}$

Answer 2

The measure of the ∠ADC in the figure, if ∠ABD =  120º is 132.0716°.

Given to us

∠ABD = 120°

What is the measure of the ∠ABD?

We know that we can apply the rule of sine rule in the ΔABD, therefore,

$\dfrac{Sin{\angle ABD}}{AD} =\dfrac{Sin{\angle ADB}}{AB}$

substitute the values,

$\dfrac{Sin\ {120^o}}{35} =\dfrac{Sin{\angle ADB}}{30}$

Sin ∠ADB = 0.7423

∠ADB = 47.928°

What are supplementary angles?

The supplementary angle are angles whose sum measure 180°

∠ADB + ∠ADC = 180°

47.928° + ∠ADC = 180°

∠ADC = 132.0716°

Hence, the measure of the ∠ADC in the figure, if ∠ABD = 120º is 132.0716°.

Learn more about Supplementary Angles:

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