Answer the following questions about the subdivision of a degree and its use in expressing angles.
(i) State the standard subdivisions of a degree in the sexagesimal system.
(ii) Explain, with reference to one complete revolution, why each degree is divided into 60 minutes and each minute into 60 seconds.
(iii) Describe, step by step, the procedure you would follow to rewrite an angle given in decimal-degree form, say θ, as D∘M′S′′ without using any built-in calculator function.
(iv) A student converts 74.508∘ directly to 74∘30′48′′ by setting up one proportion only. Point out the conceptual mistake in treating both minutes and seconds simultaneously in a single proportion and briefly indicate how the conversion should be structured.