Use the given figure to find the angle x.

In △ ADB,

AD = DB

According to isosceles triangle property,

∠DAB = ∠DBA = 36°

Using exterior angle property,

⇒ ∠DAB + ∠DBA = ∠BDC

⇒ ∠BDC = 36° + 36°

⇒ ∠BDC = 72°

In △ BDC,

DB = CB

According to isosceles triangle property,

∠BDC = ∠BCD = 72°

Sum of all angles in triangle BDC is 180°.

⇒ ∠BDC + ∠BCD + ∠CBD = 180°

⇒ 72° + 72° + ∠CBD = 180°

⇒ 144° + ∠CBD = 180°

⇒ ∠CBD = 180° - 144°

⇒ ∠CBD = 36°

Hence, the value of x = 36°.