Question

In this given figure, AD divides angle BAC in the ratio 1:3 and AD=DB.
Determine the value of x.

Answer 1

Thats the answer now

Answer 2

Step-by-step explanation:

Let angle BAD be x and angle CAD be 3x.

Then, angle EAC + angle CAD + angle BAD = 180 ...... (straight angle)

=> 108+3x+x = 180

=> 4x+108 = 180

=> 4x = 180-108

=> x = 72/4

Therefore, x = 18

So, angle BAD = 18° and angle CAD = 3×18

= 54°

and angle BAC = 54+18

= 72.

Now, AD = DB ....(given)

Therefore, angle ABC = angle BAD

So,angle ABC = 18

And in ∆ABC,

angle ABC + angle BAC + angle ACB = 180 (linear pair)

=> 18+72+x = 180

=> x = 180 - 90

Hence, x = 90°