Question

Find x :

Answer 1

Let us name the figure as following:

In ΔABC, 

AD = AC  .......[ Given ] 

∴ ∠ADC =∠ACD  ......[Angles opp. to equal sides are equal]

⇒ ∠ADC = 42°

Now, 

∠ADC = ∠DAB +∠DBA   ...[Exterior angle is equal to the sum of opp. interior angles]

But, 

∠DAB = ∠DBA  ......[Given: BD = DA]

∴ ∠ADC = 2∠DBA

⇒ 2∠DBA = 42°

⇒ ∠DBA = 21°

For x:

x = ∠CBA + ∠BCA  .......[Exterior angle is equal to the sum of opp. interior angles]

We know that,

∠CBA = 21°

∠BCA = 42°

∴ x = 21 + 42°

⇒ x = 63°