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Let's analyze the problem in detail:

### Given:
1. In triangle \( \triangle ABC \), the angle \( \angle A = 70^\circ \).
2. The internal angle \( \angle ABC \) and the external angle \( \angle ACD \) are bisected by the line that intersects at point \( E \).
3. The goal is to find the measure of \( \angle E \).

### Approach:
1. **Using the Angle Sum Property**: 
   In triangle \( \triangle ABC \), the sum of the internal angles is \( 180^\circ \). Hence, if we know one angle, we can express the other angles using that information. Let’s calculate \( \angle B \).

   \[
   \angle A + \angle B + \angle C = 180^\circ
   \]
   Since \( \angle A = 70^\circ \), we can express the sum of the remaining two angles:
   \[
   \angle B + \angle C = 110^\circ
   \]

2. **Bisection of Internal and External Angles**:
   According to the problem, the internal angle \( \angle ABC \) and the external angle \( \angle ACD \) are bisected. This suggests that point \( E \) lies on the bisector of both angles, implying that \( \angle ABE \) and \( \angle EBC \) are equal.

3. **Calculating the External Angle**:
   The external angle at \( C \) (i.e., \( \angle ACD \)) is equal to \( 180^\circ - \angle C \). So,
   \[
   \text{External angle } \angle ACD = 180^\circ - \angle C
   \]
   Since \( \angle B + \angle C = 110^\circ \), we can express \( \angle C \) as follows:
   \[
   \angle C = 110^\circ - \angle B
   \]

4. **Final Steps**: 
   From the bisector relationship, we can use properties of angle bisectors to compute the exact value of \( \angle E \).

Let me know if you want to explore more about bisectors or need further breakdowns of specific steps.

### Relative Questions:
1. How does the angle sum property help in calculating unknown angles in a triangle?
2. What is the significance of angle bisectors in a triangle?
3. Can the external angle theorem be used here to simplify the problem further?
4. How does bisection of angles influence the relations between different angles in geometry?
5. What other triangle properties can be derived from the given information?

### Tip:
Always consider both internal and external angle properties when dealing with bisectors in geometric figures to simplify the solution process.

In triangle ABC, ∠A = 70°, the internal angle ∠ABC and the external angle ∠ACD are bisected by a line intersecting at point E. What is ∠E?

This problem explores how to calculate an angle in a triangle where both an internal and an external angle are bisected. The solution uses the triangle angle sum property, external angle theorem, and angle bisector theorem. Suitable for students in Grades 8-9.

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