{"knowledge_schema": {"broad_category": "Physics \u2192 Astrophysics \u2192 Black Hole Thermodynamics", "refinement": "This problem involves calculating the entropy of a black hole based on its properties, specifically its mass and the relationship between its event horizon and entropy.", "specific_scope": "The focus is on determining the entropy of a supermassive black hole using its angular size and distance from the observer, applying concepts from black hole thermodynamics.", "goal": "Calculate the order of magnitude of the black hole's entropy to identify the correct answer from the given options."}, "summary": "This problem pertains to astrophysics and specifically to the thermodynamic properties of black holes. It requires calculating the entropy of a supermassive black hole based on its observed angular size and distance. The task involves applying the principles of black hole thermodynamics, particularly the relationship between a black hole's mass, its event horizon, and its entropy. The goal is to determine the order of magnitude of the black hole's entropy, which is found to be 10^62 J/K."}