Answers

The Brainliest Answer!
2016-01-03T22:27:16+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
QUESTION: In the ΔABC, ∠BAC=90°. If ∠ADB=120° then ∠CAD−∠ABD=?

===================================================

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 =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°.

∵ ∠CAD60°


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 = 3

------------------------------------------------------------------------------------

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°

------------------------------------------------------------------------------------

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!!
2 5 2