Final Answer:
The angles ∠1 and ∠2, forming a linear pair, have measures represented by expressions \( (4x - 1)° \) and \( (9x - 14)° \) respectively. By solving for x and substituting it back, \( m∠2 \) is found to be \( 121° \), leading to the correct answer of \( \mathbf{9°} \).
Step-by-step explanation:
In the given problem, ∠1 and ∠2 form a linear pair, meaning they are adjacent angles and their measures add up to 180°. Mathematically, this can be expressed as:
\[ m∠1 + m∠2 = 180° \]
Given that \( m∠1 = (4x - 1)° \), we substitute this expression into the equation:
\[ (4x - 1) + (9x - 14) = 180 \]
Combine like terms and solve for x:
[13x - 15 = 180]
[ 13x = 195 ]
[x = 15]
Now that we have the value of x, we can find \( m∠2 \) by substituting x back into the expression for \( m∠2 = (9x - 14)° \):
\[ m∠2 = (9(15) - 14)° = 121° \]
Therefore, the correct answer is option a) \( 9° \). The process involves understanding the properties of linear pairs, setting up an equation based on the given information, and solving for the unknown variable to determine the measure of the required angle.