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Which angles are alternate interior angles with angle 3 ? \( \angle 5 \) and \( \angle 13 \) \( \angle 7 \) and \( \angle 15 \) \( \angle 6 \) and \( \angle 16 \) \( \angle 8 \) and \( \angle 14 \)

Ask by Wheeler Pena. in the United States
Jan 24,2025

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Answer

\(\angle 5\) and \(\angle 13\) are alternate interior angles with \(\angle 3\).

Solution

To determine which angles are **alternate interior angles** with **\(\angle 3\)**, we'll consider a common geometric setup: two parallel lines intersected by a transversal. In such a configuration, alternate interior angles are pairs of angles that lie between the two parallel lines and on opposite sides of the transversal. **Here's a general labeling for reference:** ``` Parallel Line 1: A ------ B \ / \ / \ / Transversal Line: \/ /\ / \ / \ C ------ D Parallel Line 2: ``` In this setup: - **\(\angle 3\)** is formed where the transversal intersects the first parallel line. - **\(\angle 5\)** and **\(\angle 13\)** are positioned such that they lie between the two parallel lines and are on opposite sides of the transversal, making them alternate interior angles with **\(\angle 3\)**. **Therefore, the correct pair of alternate interior angles with \(\angle 3\) is:** - **\(\angle 5\) and \(\angle 13\)** **Answer:** • \(\angle 5\) and \(\angle 13\)

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Alternate interior angles are formed when a transversal crosses two parallel lines. In your scenario, angle 3 will have pairs of angles on the opposite sides of the transversal and inside the parallel lines. Therefore, identifying \( \angle 5 \) and \( \angle 13 \) as alternate interior angles would be a monitoring task to ensure they fit this definition correctly based on their relative positions. To solve problems involving alternate interior angles, visualize the two parallel lines and the transversal. Look for the pairs of angles that are on opposite sides of the transversal but inside the parallel line arrangement. A common mistake is misidentifying exterior angles as alternate interior angles, so stay keen to their positions!

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