In the structure of the antibiotic mutaxanthene a, shown below, how many trigonal planar carbon atom(s) are there?

             15 (Fifteen) trigonal planar carbon atoms.

Explanation:

Geometry around Carbon atom is basically controlled by the type of hybridization it follows. Carbon atom gives three types of hybridizations as;

Sp³ Hybridization:

                            In this type carbon atom is involved in making four single bonds with other atoms. Hence, the geometry about sp³ hybridized Carbon is tetrahedral.

Sp² Hybridization:

                            In this type carbon atom is involved in making two single bonds and one double bond with other atoms. Hence, the geometry about sp² hybridized Carbon is trigonal planar.

Sp Hybridization:

                            In this type carbon atom is involved in making one single bond and one triple bond with other atoms. Hence, the geometry about sp hybridized Carbon is linear.

Result:

           In the structure of Metaxanthene there are 15 carbons (highlighted red) which are sp² hybridized. Therefore, there are 15 trigonal planar carbons in Metaxanthene.