1. **Stating the problem:** We are given a rectangle ABCD with diagonals intersecting at point E. We know that $m\angle ADE = 16^\circ$ and $m\angle AEB = 16^\circ$. We need to find the measures of the angles $m\angle BCD$, $m\angle ADE$, $m\angle ABCD$, $m\angle AEB$, $m\angle CBE$, and $m\angle DEA$. 2. **Properties and formulas:** - In a rectangle, all angles are right angles, so $m\angle ABCD = 90^\circ$. - The diagonals of a rectangle are equal in length and bisect each other. - The diagonals form two congruent triangles. - The sum of angles around point E is $360^\circ$. 3. **Given:** - $m\angle ADE = 16^\circ$ - $m\angle AEB = 16^\circ$ 4. **Find $m\angle BCD$:** Since ABCD is a rectangle, $m\angle BCD = 90^\circ$. 5. **Find $m\angle ADE$:** Given as $16^\circ$. 6. **Find $m\angle ABCD$:** Since ABCD is a rectangle, $m\angle ABCD = 90^\circ$. 7. **Find $m\angle AEB$:** Given as $16^\circ$. 8. **Find $m\angle CBE$:** Triangles formed by diagonals are congruent. Since $m\angle AEB = 16^\circ$, $m\angle CBE$ is also $16^\circ$ by symmetry. 9. **Find $m\angle DEA$:** Since $m\angle ADE = 16^\circ$ and triangle ADE is isosceles with $AD = DE$ (diagonals bisect), $m\angle DEA = 16^\circ$. **Final answers:** $$ m\angle BCD = 90^\circ,\quad m\angle ADE = 16^\circ,\quad m\angle ABCD = 90^\circ,\quad m\angle AEB = 16^\circ,\quad m\angle CBE = 16^\circ,\quad m\angle DEA = 16^\circ $$