**Rule: Use 'an' before a word that begins with a vowel sound.** 'Eagle' starts with a vowel sound ('ee-gul'). The sentence is introducing a non-specific eagle for the first time. Therefore, the indefinite article 'an' is correct. Option (a) is wrong by sound. Option (c) would be used if the eagle had been mentioned before. Option (d) is incorrect for a singular countable noun.

**Rule: 'A great deal of' is a fixed quantifier phrase.** This expression, meaning 'a lot of', always begins with the indefinite article 'a'. It is used with uncountable nouns like 'trouble', 'time', 'money'. Options (b), (c), and (d) are incorrect for this fixed phrase.

**Rule: 'The' is used before unique celestial bodies.** Like the sun and the moon, the planet 'Earth' is considered a unique object in our solar system and takes the definite article 'the'. Sometimes it can be written without an article as a proper noun, but in this astronomical context, 'The earth' is standard. Options (a), (b), and (d) are incorrect.

**Rule: Use 'a'/'an' to denote a profession or a classification.** 'Expert' here classifies the person. 'Expert' begins with a vowel sound ('eks-pert'), so the article 'an' is required. Option (a) is wrong by sound. Option (b) would imply he is the only expert or a specific one known to all. Option (d) is incorrect as 'expert' is a singular countable noun.

**Rule: No article is used before a material noun used in its general sense.** 'Wood' is a material noun. The sentence is stating the material the chair is composed of, using 'wood' in a general sense. Therefore, no article is needed. If it were specific wood (e.g., 'The wood used in this chair is teak'), 'the' would be used. Options (a), (b), and (c) are incorrect.

**Rule: Use 'the' for unique monuments and for country names containing 'States', 'Kingdom', etc.** 'The Statue of Liberty' is a specific, unique monument and requires 'the'. 'The USA' (United States of America) is a country name that includes 'States' and therefore also requires 'the'. Both blanks must be filled with 'the'. Options (b), (c), and (d) are incorrect.

**Rule: 'By the way' is a fixed idiomatic expression.** This phrase, used to introduce a new topic or an afterthought, always uses the definite article 'the'. It is a set phrase and other articles or the omission of the article would be incorrect. Options (a), (c), and (d) are wrong.

**Rule: The definite article 'the' is used with dates, especially when written in the 'day of month' format.** The phrase 'the 26th of January' uses an ordinal number ('26th') to specify a particular day, which requires 'the'. Options (a), (b), and (d) are incorrect.

**Rule: Use 'the' when a noun has been previously mentioned or is made specific.** The book is not just any book; it is the specific one 'I borrowed from the library'. This modifying phrase makes the noun definite, so 'the' is required. Option (a) would introduce a new, unspecified book. Option (b) is wrong by sound. Option (d) is not used for singular countable nouns.

**Rule: 'The' is used in the expression 'the kind of', 'the sort of', 'the type of' when followed by a defining clause.** The clause 'who would cheat' defines the kind of person. This makes the 'kind' specific, requiring 'the'. In contrast, a question like 'What kind of person is he?' takes no article. But in this declarative, defining sentence, 'the' is correct. Options (a), (b), and (d) are incorrect for this structure.