1. The problem asks if lines $j$ and $k$ are parallel and to explain the reasoning. 2. From the graph description, lines $j$ and $k$ are marked as parallel ($j \parallel k$). 3. The angles given are 35° and 110° at intersections formed by a transversal with lines $j$ and $k$. 4. When two lines are cut by a transversal, if corresponding angles or alternate interior angles are equal, the lines are parallel. 5. Here, the 35° and 110° angles are supplementary ($35° + 110° = 145°$), which is not 180°, so these are not supplementary angles. 6. However, the problem states $j \parallel k$ explicitly, so by definition, $j$ is parallel to $k$. --- 7. The second problem asks to find the number of sides of a regular polygon whose interior angle measures 140°. 8. The formula for the measure of each interior angle of a regular polygon with $n$ sides is: $$\text{Interior angle} = \frac{(n-2) \times 180°}{n}$$ 9. Substitute 140° for the interior angle: $$140 = \frac{(n-2) \times 180}{n}$$ 10. Multiply both sides by $n$: $$140n = 180(n-2)$$ 11. Distribute 180: $$140n = 180n - 360$$ 12. Subtract 180n from both sides: $$140n - 180n = -360$$ $$-40n = -360$$ 13. Divide both sides by -40: $$n = \frac{-360}{-40} = 9$$ 14. Therefore, the polygon has 9 sides. Final answers: - Lines $j$ and $k$ are parallel as given. - The polygon has 9 sides.