In the following figure, find the value of x:

△ABD is an isosceles triangle with BD = AD,

∴ ∠DBA = ∠BAD = 48°.

We know that,

An exterior angle is equal to the sum of two opposite interior angles,

Ext. ∠ADC = ∠BAD + ∠DBA = 48° + 48° = 96°.

△ADC is an isosceles triangle with AD = DC,

∴ ∠DAC = ∠DCA = x°.

Since, sum of angles of triangle = 180°.

Considering △ADC we get,

⇒ ∠DAC + ∠ADC + ∠DCA = 180°

⇒ x° + 96° + x° = 180°

⇒ 2x° + 96° = 180°

⇒ 2x° = 180° - 96° = 84°

⇒ x° = 42°

Hence, x = 42°.