1. **Stating the problem:** We need to find the values of angles $h$ and $j$ formed by two intersecting chords inside a circle, given one angle is $39^\circ$ and the other angles are related. 2. **Relevant formula:** When two chords intersect inside a circle, the measure of each angle formed is half the sum of the measures of the intercepted arcs. 3. **Important rule:** Vertical angles formed by intersecting chords are equal. 4. **Step 1:** Since the angle adjacent to $h$ is $39^\circ$, and $h$ is its vertical angle, we have: $$h = 39^\circ$$ 5. **Step 2:** Angles $h$ and $j$ form a linear pair, so they are supplementary: $$h + j = 180^\circ$$ 6. **Step 3:** Substitute $h = 39^\circ$ into the equation: $$39^\circ + j = 180^\circ$$ 7. **Step 4:** Solve for $j$: $$j = 180^\circ - 39^\circ = 141^\circ$$ **Final answers:** $$h = 39^\circ$$ $$j = 141^\circ$$