In the adjoining figure, BD= AD = AC. If ∠ABD = 36°, find the value of x.

From figure,

∠ABD = ∠BAD = 36° (As angles opposite to equal sides are equal.)

∠BDA = 180° - (36° + 36°) = 180° - 72° = 108°.

From figure,

∠BDA + ∠ADC = 180°

108° + ∠ADC = 180°

∠ADC = 72°.

In △ADC,

As AD = AC,

∴ ∠ADC = ∠ACD = 72° (As angles opposite to equal sides are equal.)

∠ADC + ∠ACD + ∠DAC = 180°

72° + 72° + ∠DAC = 180°

∠DAC = 180° - 144° = 36°.

From figure,

∠BAD + ∠DAC + x = 180°

36° + 36° + x = 180°

72° + x = 180°

x = 108°.

Hence, x = 108°.