Question

Letters a, b, c, and d are angle measures. Which should equal 105° to prove that f / g?

a) 75°
b) 6°
c) n
d) o

Answer 1

Main Answer:

The angle measure that should equal 105° to prove
`\(f / g\) is option (b) 6°.`

Therefore, the correct answer is b) 6°.

Explanation:

To demonstrate that
`\(f / g\)` is equal to 105°, we need to consider the supplementary angles formed by the given angle measures. The sum of angles that form a straight line is 180°. If we let the unknown angle be
`\(n\),` then the relationship between the angles can be expressed as:

`\[ a + b + c + d + n = 180^\circ \]`

Since we are interested in
`\(f / g\)`being equal to 105°, we can infer that
`\(f = n\) and \(g = 180^\circ - n\). So, \(f / g\)` is equivalent to:

`\[ (n)/(180^\circ - n) \]`

The given options are
`\(a) 75°\), \(b) 6°\), \(c) n\),` and
`\(d) o\).` To find the correct value of \(n\), we set up the equation:

`\[ 6° / (180^\circ - 6°) = 105^\circ \]`

Solving this equation, we find that
`\(n\) (or \(f\))` is indeed 6°, making option (b) the correct choice. Therefore, option (b) 6° is the angle measure that should equal 105° to prove
`\(f / g\).`

Therefore, the correct answer is b) 6°.