1. The problem gives three angle measures in terms of $x$: $m\angle LJK = 6x$, $m\angle FEB = 7x - 7$, and $m\angle GIA = 4x - 2$. We are asked to find the value of $x$ or the measures of these angles. 2. Since these angles are likely related by the geometry of the figure (e.g., they might be angles around a point or in a triangle), we use the fact that the sum of angles around a point is $360^\circ$ or the sum of angles in a triangle is $180^\circ$. Without explicit relationships, we assume these three angles sum to $180^\circ$ as a common case. 3. Write the equation: $$6x + (7x - 7) + (4x - 2) = 180$$ 4. Simplify the left side: $$6x + 7x - 7 + 4x - 2 = 180$$ $$ (6x + 7x + 4x) + (-7 - 2) = 180$$ $$17x - 9 = 180$$ 5. Solve for $x$: $$17x = 180 + 9$$ $$17x = 189$$ $$x = \frac{189}{17}$$ $$x \approx 11.12$$ 6. Find each angle measure: - $m\angle LJK = 6x = 6 \times 11.12 = 66.7^\circ$ - $m\angle FEB = 7x - 7 = 7 \times 11.12 - 7 = 77.84 - 7 = 70.84^\circ$ - $m\angle GIA = 4x - 2 = 4 \times 11.12 - 2 = 44.48 - 2 = 42.48^\circ$ 7. Check sum: $$66.7 + 70.84 + 42.48 = 180.02^\circ$$ (close to 180, rounding error) Final answer: $x = \frac{189}{17} \approx 11.12$, with angles approximately $66.7^\circ$, $70.84^\circ$, and $42.48^\circ$ respectively.