1. **Stating the problem:** We are given a quadrilateral ABCD with diagonals AC and BD intersecting at point E. We need to find the measures of angles $\angle BCD$, $\angle ABD$, $\angle CBE$, $\angle ADE$, $\angle AEB$, and $\angle CEA$. The angle $\angle DEA$ is given as 16°. 2. **Understanding the figure and properties:** Since E is the intersection of diagonals AC and BD, angles around E have relationships. Also, $\angle DEA = 16^\circ$ is given. 3. **Using vertical angles:** At the intersection E, vertical angles are equal. So, $$m\angle DEA = m\angle BEC = 16^\circ.$$ 4. **Using linear pairs:** Angles on a straight line sum to 180°. For example, on line AC, $$m\angle CEA + m\angle DEA = 180^\circ.$$ Given $m\angle DEA = 16^\circ$, then $$m\angle CEA = 180^\circ - 16^\circ = 164^\circ.$$ 5. **Similarly, on line BD,** $$m\angle AEB + m\angle BEC = 180^\circ.$$ Given $m\angle BEC = 16^\circ$, then $$m\angle AEB = 180^\circ - 16^\circ = 164^\circ.$$ 6. **Using triangle angle sum:** Consider triangle ADE. The sum of interior angles is 180°. $$m\angle ADE + m\angle DEA + m\angle EAD = 180^\circ.$$ We know $m\angle DEA = 16^\circ$, but $m\angle EAD$ is not given, so we cannot find $m\angle ADE$ without more information. 7. **Similarly, for other angles $\angle BCD$, $\angle ABD$, and $\angle CBE$,** without additional information or measurements, we cannot determine their exact values. **Final answers:** $$m\angle DEA = 16^\circ$$ $$m\angle BEC = 16^\circ$$ $$m\angle CEA = 164^\circ$$ $$m\angle AEB = 164^\circ$$ Other angles cannot be determined with the given information.