Given,
AB divides ∠DAC in the ratio 1: 3
∠DAB: ∠BAC = 1: 3
∠DAC + ∠EAC = 180°
∠DAC + 108° = 180°
∠DAC = 180° – 108°
= 72°
∠DAB = \(\frac{1}{4}\) x 72° = 18°
∠BAC = \(\frac{3}{4}\) x 72° = 54°
In ΔADB
∠DAB + ∠ADB + ∠ABD = 180°
18° + 18° + ∠ABD = 180°
36° + ∠ABD = 180°
∠ABD = 180° – 36°
= 144°
∠ABD + ∠ABC = 180°(Linear pair)
144° + ∠ABC = 180°
∠ABC = 180° – 144°
= 36°
In ΔABC
∠BAC + ∠ABC + ∠ACB = 180°
54° + 36° + x = 180°
90° + x = 180°
x = 180° – 90°
= 90°
Thus, x = 90°