The presentation of burning mouth, depapillation of the tongue (atrophic glossitis), and angular cheilitis strongly suggests a Vitamin B12 deficiency. Vitamin B12 is essential for maintaining the integrity of the oral mucosa and nerve function. Deficiency leads to mucosal atrophy, causing a smooth, sore tongue and burning sensation. Angular cheilitis arises from mucosal breakdown and secondary infection. These findings are classic in Vitamin B12 deficiency anemia and are less prominent in other deficiencies.

Reference: Oral Pathology, Neville et al., 4th Edition.