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In this problem, we know that triangles \( \triangle JKL \) and \( \triangle DEF \) are similar. This means that their corresponding angles are equal.

Given dataIn this problem, we know that triangles \( \triangle JKL \) and \( \triangle DEF \) are similar. This means that their corresponding angles are equal.

Given 
- \( m \angle J = 62^\circ \)
- \( m \angle F = 70^\circ \)

Since these triangles are similar, their corresponding angles will match:
- \( m \angle J = m \angle D \)
- \( m \angle K = m \angle E \)
- \( m \angle L = m \angle F \)

Since \( m \angle F = 70^\circ \), we conclude that \( m \angle L = 70^\circ \).

Now we can find \( m \angle E \), which corresponds to \( m \angle K \), by using the angle sum property of a triangle. The sum of all angles in any triangle is \(180^\circ\).

### Calculation:
\[
m \angle J + m \angle K + m \angle L = 180^\circ
\]
Substitute the known values:
\[
62^\circ + m \angle K + 70^\circ = 180^\circ
\]
\[
m \angle K = 180^\circ - 62^\circ - 70^\circ
\]
\[
m \angle K = 48^\circ
\]

Therefore, \( m \angle E = 48^\circ \).

### Answer:
The correct answer is:
**48**

Would you like more details or have any questions?

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Here are some related questions:
1. If \( \triangle JKL \sim \triangle DEF \), what does this imply about the ratio of their sides?
2. How do we know that the angle sum property of a triangle is always 180 degrees?
3. If \( m \angle K \) were known, could we find \( m \angle J \) instead?
4. What other information can be derived from similar triangles besides angle measures?
5. How can we determine if two triangles are similar based on their angles alone?

**Tip:** In similar triangles, corresponding angles are equal, and corresponding sides are proportional.

When ∆JKL ~ ∆DEF the m∠J = 62 and the m∠F = 70. What is the m∠E?

Learn how to determine the measure of an angle in similar triangles ∆JKL and ∆DEF, given m∠J = 62° and m∠F = 70°. This problem covers the similarity of triangles, angle sum property, and properties of corresponding angles. Suitable for students in Grades 8-10.

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