In the following figure, find the value of x:

From figure,

∠ACD = 180° - 130° = 50°.

In △ADC, AD = CD.

∴ ∠DAC = ∠ACD = 50°.

∠ADC = 180° - (∠CAD + ∠DCA) = 180° - (50° + 50°) = 80°.

From figure,

∠ADB + ∠ADC = 180°

∠ADB = 180° - ∠ADC = 180° - 80° = 100°.

In △ADB,

∠DBA = ∠DAB = x° (As angles opposite to equal sides are equal)

∠DBA + ∠DAB + ∠ADB = 180°

x° + x° + 100° = 180°

2x° = 80°

x° = 40°

Hence, x = 40°.