https://file.aiquickdraw.com/mathbot/file/17273550107553m4r06ht.jpg

Let's analyze the diagram and the problem.

We are asked to find \( m\angle 2 \) given that \( m\angle 4 = 35^\circ \), and we must explain the reasoning behind the choice.

### Observations from the Diagram:
1. The diagram shows a parallelogram \( ABCD \).
2. The line \( AB \) is parallel to line \( CD \), and the transversal is \( BD \), forming the angles \( \angle 2 \) and \( \angle 4 \).
3. From geometry, we know that if two lines are parallel, alternate interior angles are equal.

Thus, since \( \angle 2 \) and \( \angle 4 \) are alternate interior angles, they must be equal. Therefore, \( m\angle 2 = m\angle 4 \).

Since \( m\angle 4 = 35^\circ \), it follows that \( m\angle 2 = 35^\circ \).

### Answer:
The correct answer is **D**: \( \angle 2 \) and \( \angle 4 \) are alternate interior angles, so \( m\angle 2 = m\angle 4 = 35^\circ \).

Would you like further clarification or details? Here are some related questions:

1. What are alternate interior angles, and how do they work in parallel line systems?
2. Can corresponding angles also be used to solve such problems?
3. How do we prove two angles are supplementary?
4. What is the difference between complementary and supplementary angles?
5. Are there any other ways to confirm \( m\angle 2 = 35^\circ \)?

**Tip:** Always remember the relationship between angles formed by parallel lines and transversals, as it is frequently used in geometric problems.

In this geometry problem, we are asked to find the value of m∠2 given that m∠4 = 35°. Learn how to apply the Alternate Interior Angle Theorem to solve for m∠2 in parallel lines. This is suitable for students in Grades 8-10.

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