In the ΔABC, ∠BAC=90. If ∠ADB=120 then ∠CAD−∠ABD=?
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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.
------------------------------------------------------------------------------------
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
°.
∠ADB + ∠ADC = 180°
let ∠ADC be
.
So,
°
°
let alone the degrees, for a while.
=>
=>
=>
∴
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
.
also, let alone the degrees, for a while.

=>
=>
=>
∴
is equal to 30°.
Therefore, the value of ∠ABD is 30°.
∵ ∠ABD = 30°
------------------------------------------------------------------------------------
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.
= 
=
∴ ∠CAD - ∠ABD = 30°
------------------------------------------------------------------------------------
Answer: ∠CAD-∠ABD is equal to 30°.
------------------------------------------------------------------------------------
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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.
------------------------------------------------------------------------------------
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
∠ADB + ∠ADC = 180°
let ∠ADC be
So,
let alone the degrees, for a while.
=>
=>
=>
∴
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
also, let alone the degrees, for a while.
=>
=>
=>
∴
Therefore, the value of ∠ABD is 30°.
∵ ∠ABD = 30°
------------------------------------------------------------------------------------
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.
=
=
∴ ∠CAD - ∠ABD = 30°
------------------------------------------------------------------------------------
Answer: ∠CAD-∠ABD is equal to 30°.
------------------------------------------------------------------------------------
HOPE THAT HELPS YOU!!!
PLZ MARK ANSWER AS BRAINILIEST :-)))
Or, PRESS ON "THANKS" BUTTON!!
SPEND A NICE DAY. ENJOY WORKING WITH BRAINLY :-PP
WISH YOU A HAPPY NEW YEAR AND A BEST 2016 FOR YOU!!
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