you know how alternate angles between parralell lines are equal, how come the alternate angle between those towo paralled lines did not work as the answer given from that reasoning would give 12

Alternate angles are equal when a transversal crosses two parallel lines. However, it's important to correctly identify and apply this rule. If the alternate angle doesn't give the expected answer (in your case, 12), several issues might be the cause:

1. **Incorrect identification of angles**: Make sure you're identifying alternate angles correctly. Alternate angles are those on opposite sides of the transversal but between the two parallel lines.

2. **Incorrect use of the alternate angle rule**: The rule states that alternate interior angles are equal, not just any angles formed by the transversal.

3. **Misinterpretation of the problem**: Ensure that the problem setup actually involves parallel lines and a transversal. If the lines aren't parallel, the alternate angle rule doesn't apply.

4. **Incorrect initial value**: Double-check the angles or values given in the problem. A mistake in the initial information can lead to an incorrect application of the alternate angle rule.

If you found an angle using the alternate angle rule and got 12, but the answer doesn't match the expected result, recheck the problem for one of these issues. It's likely that either the identification of the angles or the setup of the problem was incorrect.

Would you like to go through a specific example or problem to understand where the error occurred?

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Do you want further details or have any questions? Here are some related questions:

1. How do you identify alternate interior angles in a diagram?
2. What are some common mistakes when applying the alternate angle rule?
3. Can you explain the difference between alternate interior and corresponding angles?
4. How do you prove that alternate interior angles are equal?
5. What happens if the lines are not parallel when using the alternate angle rule?

**Tip:** Always ensure the lines are truly parallel before applying any angle-related rules involving transversals.

you know how alternate angles between parallel lines are equal, how come the alternate angle between those two parallel lines did not work as the answer given from that reasoning would give 12

Explore why alternate interior angles are equal when two parallel lines are crossed by a transversal, and why an incorrect angle might be obtained. This guide covers common mistakes and the correct application of the Alternate Interior Angles Theorem, suitable for students in Grades 6-8.

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