The spelling of the word "art angry" can be explained using IPA (International Phonetic Alphabet). "Art" is pronounced as /ɑːt/, with the symbol "ɑː" representing an open back unrounded vowel. "Angry" is pronounced as /ˈæŋɡri/, with the symbol "æ" representing a near-open front unrounded vowel and "ŋ" representing a velar nasal consonant. Therefore, the correct spelling of "art angry" includes the letter "r" in "art" and the letter "g" in "angry", with each letter accurately reflecting its respective IPA sound.