In the following figure, find the value of x:

△BDC is an isosceles triangle with BD = DC,

∴ ∠DBC = ∠DCB = 27°.

We know that,

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

Ext. ∠ADC = ∠DBC + ∠DCB = 27° + 27° = 54°.

△ADC is an isosceles triangle with AC = DC,

∴ ∠DAC = ∠ADC = 54°.

Since, sum of angles of triangle = 180°.

Considering △ADC we get,

⇒ ∠DAC + ∠ADC + ∠DCA = 180°

⇒ 54° + 54° + x = 180°

⇒ x + 108° = 180°

⇒ x = 180° - 108° = 72°.

Hence, x = 72°.