1. **Problem Statement:** We are given a circle with points F, G, H, and A on its circumference. Triangle FGH is inscribed in the circle. The segment GH measures $21x - 2$ and segment FA measures $38x + 5$. We need to find the length of segment $mFGH$ (interpreted as the measure of arc $FGH$ or the length of segment $FGH$ depending on context). 2. **Understanding the Problem:** Since $F, G, H, A$ lie on the circle, and $FGH$ is a triangle inscribed in the circle, the segments $FG$, $GH$, and $FH$ are chords of the circle. We are given $GH = 21x - 2$ and $FA = 38x + 5$. However, $FA$ is not part of triangle $FGH$, so it might be used to find $x$ if $FA$ and $GH$ are related. 3. **Assumption:** If $FA$ and $GH$ are equal chords (or related by some property), we can set $21x - 2 = 38x + 5$ to solve for $x$. 4. **Solve for $x$:** $$21x - 2 = 38x + 5$$ $$21x - 38x = 5 + 2$$ $$-17x = 7$$ $$x = -\frac{7}{17}$$ 5. **Calculate $GH$:** $$GH = 21x - 2 = 21 \times \left(-\frac{7}{17}\right) - 2 = -\frac{147}{17} - 2 = -\frac{147}{17} - \frac{34}{17} = -\frac{181}{17} \approx -10.65$$ 6. **Interpretation:** Lengths cannot be negative, so our assumption that $FA = GH$ is incorrect or incomplete. More information is needed to solve for $mFGH$. **Conclusion:** Without additional information or relationships between the segments, $mFGH$ cannot be determined from the given data.