1. **State the problem:** Given that $m\angle BHG = 100^\circ$, find $m\angle CED$ in the given quadrilateral with intersecting diagonals and marked congruent segments and right angles. 2. **Analyze the diagram and given information:** - $\angle BHG$ is given as $100^\circ$. - There are congruent segments marked: $AC \cong BH$, $CD \cong DG$, and $FG \cong GJ$. - $\angle D$ and $\angle J$ are right angles ($90^\circ$). - The quadrilateral and its diagonals create several triangles and angles. 3. **Use properties of congruent segments and angles:** - Since $AC \cong BH$, triangles involving these segments may be congruent or isosceles. - Right angles at $D$ and $J$ help identify perpendicular lines. 4. **Relate $\angle BHG$ to $\angle CED$:** - $\angle BHG$ and $\angle CED$ are vertical angles formed by the intersection of diagonals. - Vertical angles are congruent. 5. **Conclusion:** - Therefore, $m\angle CED = m\angle BHG = 100^\circ$. **Final answer:** $$m\angle CED = 100^\circ$$