Question

4 what is the value of \\( \angle f \\)?

Explanation:

Step1: Find the measure of $\angle FEG$

Since $\angle MEF = 94^{\circ}$ and $\angle MEF+\angle FEG = 180^{\circ}$ (linear - pair of angles), then $\angle FEG=180^{\circ}- 94^{\circ}=86^{\circ}$.

Step2: Use the angle - sum property of a triangle

In $\triangle FEG$, we know that the sum of interior angles of a triangle is $180^{\circ}$. Let $\angle F=x$. Then $x+\angle FEG+\angle G = 180^{\circ}$.
Substitute $\angle FEG = 86^{\circ}$ and $\angle G = 54^{\circ}$ into the equation: $x+86^{\circ}+54^{\circ}=180^{\circ}$.
Simplify the left - hand side: $x + 140^{\circ}=180^{\circ}$.
Solve for $x$: $x=\angle F=180^{\circ}-140^{\circ}=40^{\circ}$.

Answer:

C. 40