Elementary Geometry for College Students (6th Edition)

m$\angle$FAE is not clearly noted as being obtuse.
m$\angle$FAB + m$\angle$BAE = the larger m$\angle$ FAE The claim provided (m$\angle$FAB + m$\angle$BAE = m$\angle$ FAE) implies m$\angle$ FAE is less than 180. Therefore, since m$\angle$ FAE is not specified to be greater than 180, the claim is wrong.