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In the given problem, we have an isosceles triangle \( \triangle CDE \) where \( EC \cong DE \) and \( \angle D = 73^\circ \). We are asked to find \( m \angle E \).

### Solution:

1. Since \( \triangle CDE \) is isosceles with \( EC \cong DE \), angles opposite these sides will be equal. Thus, \( \angle C = \angle E \).

2. We know the sum of all angles in any triangle is \( 180^\circ \).

   \[
   m \angle C + m \angle D + m \angle E = 180^\circ
   \]

3. Substitute \( m \angle D = 73^\circ \) and recognize that \( m \angle C = m \angle E \).

   \[
   m \angle E + 73^\circ + m \angle E = 180^\circ
   \]

4. Combine like terms:

   \[
   2 \cdot m \angle E = 180^\circ - 73^\circ
   \]

5. Simplify the right side:

   \[
   2 \cdot m \angle E = 107^\circ
   \]

6. Divide by 2 to solve for \( m \angle E \):

   \[
   m \angle E = \frac{107^\circ}{2} = 53.5^\circ
   \]

### Answer:
\( m \angle E = 53.5^\circ \)

Would you like more details on any part of this solution, or have any other questions?

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Here are five related questions to deepen understanding:

1. How would the solution change if \( \angle D \) were different?
2. What properties of isosceles triangles are useful in solving such problems?
3. How would you verify if \( \triangle CDE \) is an isosceles triangle if you only knew two angles?
4. What would \( m \angle E \) be if \( \triangle CDE \) were an equilateral triangle?
5. Can you solve for \( m \angle E \) if given \( \angle C = 60^\circ \) and \( \angle D = 50^\circ \)?

**Tip:** In isosceles triangles, the base angles (opposite the equal sides) are always equal, making them useful for finding unknown angles when given one angle.

In ΔCDE, EC ≅ DE and m∠D = 73°. Find m∠E.

Learn how to find m∠E in an isosceles triangle ΔCDE where EC ≅ DE and m∠D = 73°. This problem covers essential geometry concepts, including triangle angle sum and properties of isosceles triangles. Suitable for students in Grades 7-10.

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