1. **State the problem:** We are given a triangle $\triangle FGH$ with angles $m\angle F = (5x - 16)^\circ$, $m\angle G = (2x - 13)^\circ$, and $m\angle H = (8x + 14)^\circ$. We need to find the measure of angle $H$. 2. **Recall the triangle angle sum property:** The sum of the interior angles of any triangle is always $180^\circ$. So, $$m\angle F + m\angle G + m\angle H = 180^\circ$$ 3. **Set up the equation:** Substitute the given expressions: $$ (5x - 16) + (2x - 13) + (8x + 14) = 180 $$ 4. **Combine like terms:** $$ 5x + 2x + 8x - 16 - 13 + 14 = 180 $$ $$ (5x + 2x + 8x) + (-16 - 13 + 14) = 180 $$ $$ 15x - 15 = 180 $$ 5. **Solve for $x$:** $$ 15x - 15 = 180 $$ Add 15 to both sides: $$ 15x - \cancel{15} + 15 = 180 + 15 $$ $$ 15x = 195 $$ Divide both sides by 15: $$ \frac{\cancel{15}x}{\cancel{15}} = \frac{195}{15} $$ $$ x = 13 $$ 6. **Find $m\angle H$ by substituting $x=13$ into $8x + 14$:** $$ m\angle H = 8(13) + 14 = 104 + 14 = 118^\circ $$ **Final answer:** $$ m\angle H = 118^\circ $$