# Chapter 2 - Reasoning and Proof - 2-5 Reasoning in Algebra and Geometry - Practice and Problem-Solving Exercises - Page 118: 24

\begin{array}{c|ll}& \textbf{Statement} & \textbf{Reasons} \\\hline1 & \text{m}\angle{GFI} \text{ = 128} & \text{Given} \\2 & \text{m}\angle{GFE}\text{ + m}\angle{EFI}\text{ = m}\angle{GFI} & \text{Angle Addition Postulate} \\3 & \text{9x - 2 + 4x = 128} & \text{Substitution Property} \\4 & \text{13x - 2 = 128} & \text{Distributive Property} \\5 & \text{13x = 130} & \text{Addition Property of Equality} \\6 & \text{x = 10} & \text{Division Property of Equality} \\7 & \text{m}\angle{EFI}\text{ = 4x} & \text{Given} \\8 & \text{m}\angle{EFI}\text{ = 4(10)} & \text{Substitution Property} \\9 & \text{m}\angle{EFI}\text{ = 40} & \text{Simplify} \end{array}

#### Work Step by Step

Substitute the measures shown in the diagram and solve for x. Use the value you found for x to find $m\angle {EFI}$.

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