If 2 angles: ABC=60° and DCE=120° (adds up to 180° so it's parallel) and I'm answering a question,how do I write the $$  $$"Reason" for it?

When you're explaining why two lines are parallel based on the angles, you need to clearly state the geometric principle that justifies this conclusion. Here's how you can write the reason:

**Reason:** "Since the sum of the angles $ \angle ABC = 60^\circ $ and $ \angle DCE = 120^\circ $ is $ 180^\circ $, the lines are parallel by the **Converse of the Interior Angles Theorem**."

The **Converse of the Interior Angles Theorem** states that if two lines are cut by a transversal and the sum of the interior angles on the same side of the transversal is $180^\circ$, then the lines are parallel.

If you have any questions or want more details on this concept, feel free to ask!

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Here are five related questions:
1. What is the Converse of the Alternate Interior Angles Theorem?
2. How do you prove two lines are parallel using corresponding angles?
3. What is the difference between supplementary and complementary angles?
4. How can you determine if two lines are perpendicular using angle measurements?
5. What are the properties of parallel lines in a trapezoid?

**Tip:** Always remember to explicitly state the geometric theorems or postulates you use in your reasoning for clarity and correctness.

Understand how to justify parallel lines based on angle sums in geometry. Explore the Converse of the Interior Angles Theorem with an example where angles ABC and DCE add up to 180°, leading to parallel lines.

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