Final answer:
Photosynthetic dinoflagellates have chloroplasts with four membranes due to secondary endosymbiosis with a red alga, a feature that differentiates them from typical two-membrane chloroplasts found in primary photosynthetic organisms.
Step-by-step explanation:
The chloroplasts in photosynthetic dinoflagellates are unique due to their origin via secondary endosymbiosis involving a red alga. Unlike the 'typical' chloroplasts in many other photosynthetic organisms, which possess two membranes, dinoflagellate chloroplasts are distinguished by having four membranes. This extra membrane is a result of the engulfing and assimilating process of the red alga by the heterotrophic eukaryote precursor of the dinoflagellates.
The extra membrane supports the hypothesis that these chloroplasts were not descended but acquired from a common photosynthetic endosymbiont, resulting in the capability of some dinoflagellates to perform photosynthesis. Additionally, many dinoflagellates have a theca made of cellulose plates and two flagella contributing to their characteristic spinning motion.