芸術 and 美術: Music within art and studying fine arts
Read music as one of the arts, then distinguish studying 美術 from seeing a student exhibition at an art museum.
Music as one of the arts
芸術（げいじゅつ） means art. 「町の芸術祭で妹の絵が展示された。」 means “My younger sister's painting was displayed at the town art festival.” The displayed object is the younger sister’s painting; its display does not identify when it was painted.
「音楽も生活を豊かにする芸術の一つだ。」 means “Music is also an art that enriches life.” 芸術の一つ includes music among the arts. The sentence does not restrict art to pictures.
Studying and viewing fine arts
美術（びじゅつ） means art or fine arts. 「妹は学校で美術を勉強しています。」 means “My younger sister studies art at school.” The school is the place of study, while 美術 is the subject studied.
「町の美術館で学生の作品展を見た。」 means “I saw a student exhibition at the town art museum.” 美術館 names the location, and 作品展 identifies the exhibition seen. Studying art and seeing an exhibition are different actions.
Read the field and its target
The 芸術 examples present a painting’s display and the inclusion of music. The 美術 examples present study and exhibition viewing. Even when both words have the English meaning art, their surrounding words identify the target.
音楽も and 芸術の一つ provide the inclusion relationship. An exhibition’s location does not define every artistic medium, and studying 美術 does not itself report visiting an exhibition.
Does 音楽も生活を豊かにする芸術の一つだ exclude music from art?
Show the answer and why
No. It explicitly presents music as one of the arts. Studying 美術 at school identifies a subject of study without restricting all art to pictures.