Question

In the ΔABC, ∠BAC=90. If ∠ADB=120 then ∠CAD−∠ABD=?

Answer 1

QUESTION: In the ΔABC, ∠BAC=90°. If ∠ADB=120° then ∠CAD−∠ABD=?

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ANSWER: 

To find the difference of the angles of ∠CAD and ∠ABD, we have to follow the steps below:

1. Firstly, we have to find the respective values of:
                    a. ∠CAD
                    b. ∠ABD

2. Lastly, we have to subtract the angle of ∠ABD from the angle of ∠CAD.

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1. FINDING RESPECTIVE VALUES OF SPECIFIC ANGLES

a. The value of ∠CAD

The question says that ∠CAD is equal to ∠ADC.

So, we have to find the value of ∠ADC.

We know, ∠ADB $=120$°.

∠ADB + ∠ADC = 180°

let ∠ADC be $x$.

So, $120$° $+x=180$°
let alone the degrees, for a while.

=>  $120+x=180$

=>  $x=180-120$

=>  $x=60$

∴ $x$ is equal to 60°.

That means, the value of ∠ADC is 60°.
Therefore, the value of ∠CAD is also 60°.

∵ ∠CAD = 60°


b. The value of ∠ABD

We know, ∠a + ∠b + ∠c = 180°
Theorem: The sum of all angles in a triangle is always equal to 180°.

So, ∠ABD + ∠BAC + ∠CAD = 180°

let ∠ABD be $y$.
also, let alone the degrees, for a while.

$y+90+60=180$

=>  $y+150=180$

=>  $y=180-150$

=>  $y=30$

∴ $y$ is equal to 30°.
Therefore, the value of ∠ABD is 30°.

∵ ∠ABD = 30°

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2. THE DIFFERENCE OF THE SPECIFIC ANGLES

To find the difference of the angles of ∠CAD and ∠ABD, we have to subtract ∠ABD from ∠CAD.

 ∠CAD - ∠ABD 

= 60° - 30°

let alone the degrees, for a while.

=  $60-30$

=  $30$

∴  ∠CAD - ∠ABD = 30°

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Answer: ∠CAD-∠ABD is equal to 30°.

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