1. **State the problem:** We are given a circle with chords intersecting inside it. The measures of arcs $FJ$ and $GH$ are $84^\circ$ and $76^\circ$ respectively. We need to find the measure of angle $\angle HKJ$ formed by the intersection of chords $GJ$ and $FH$ at point $K$. 2. **Formula used:** When two chords intersect inside a circle, the measure of the angle formed is half the sum of the measures of the intercepted arcs. Specifically, $$\angle HKJ = \frac{1}{2} (\text{arc } FJ + \text{arc } GH)$$ 3. **Apply the formula:** Substitute the given arc measures: $$\angle HKJ = \frac{1}{2} (84^\circ + 76^\circ)$$ 4. **Calculate the sum inside the parentheses:** $$84^\circ + 76^\circ = 160^\circ$$ 5. **Calculate the angle:** $$\angle HKJ = \frac{1}{2} \times 160^\circ = 80^\circ$$ 6. **Conclusion:** The measure of $\angle HKJ$ is $80^\circ$. **Note:** The provided answer "50" does not match the calculation based on the given arcs and the chord intersection angle theorem.