Final answer:
The story about solving Agnes Botherwood's murder is categorized as a detective story, which is a sub-genre of crime fiction focusing on the investigation of crimes.
Step-by-step explanation:
The story beginning with a policeman investigating the murder of Agnes Botherwood falls under the detective story genre. This genre is part of a broader category known as crime fiction, where the narrative is centered around criminal acts, the subsequent investigation, and the resolution. Within detective stories, certain elements are commonly present, including a crime, a criminal, and a detective or investigator working to solve the crime.
Often, these stories involve logical reasoning, clues, red herrings, and suspense as the detective uncovers the truth. Other genres related to detective stories can include mystery, thriller, and sometimes horror, especially when the narrative employs elements like psychological suspense or fear.