I have some thoughts of my own. However, I am not certain if they are correct.
The key to the question certainly cannot lie in the electronic factor because the cis- and trans- isomers do not differ in this aspect, except for the difference in the overall dipole moment. Thus, I believe we can only rationalise this with steric considerations. Let's first take a look at the chemical structures.
Fig. 1: Structure of tiglic acid
Fig. 2: Structure of angelic acid
The steric interaction I would like to focus on is the repulsion between the methyl groups and the negatively-charged oxygen atom of the carboxylate ion. Due to resonance, the negative charge would be delocalised over the two oxygen atoms of the carboxylate ion conjugate base. In the trans-isomer (angelic acid), the methyl group is located closer to one of the oxygen atoms (i.e. the oxygen atom of the carbonyl group). Thus, there would be a stronger repulsive interaction between the two. In the cis-isomer (tiglic acid), the methyl group is located further away from that oxygen atom, thus the intramolecular repulsion would be lessened, thus it is more stable.
Since a more stable conjugate base implies that the acid is stronger, the cis-isomer (tiglic acid) is more acidic than the trans-isomer (angelic acid). This argument is in full agreement with the information presented in your reference book.