“If two angles are (Select)  of the same angle, then the two angles are (Select) ."

The complete sentence could be: 

"If two angles are **supplements** of the same angle, then the two angles are **congruent**."

This is because if two angles are supplementary to the same angle, their measures must add up to the same value (180° minus the measure of the common angle), implying that the two angles are equal in measure.

Would you like more details or have any questions about this?

Here are 5 related questions for further exploration:
1. What is the difference between complementary and supplementary angles?
2. How can you prove that two angles are congruent using the concept of supplements?
3. What are vertical angles, and why are they congruent?
4. How do you find the measure of an unknown angle if you know it's a supplement of another angle?
5. Can two obtuse angles ever be supplementary? Why or why not?

**Tip**: Congruent angles always have the same measure, regardless of their orientation or position!

If two angles are (Select) of the same angle, then the two angles are (Select).

Explore the concept of supplementary angles and how two angles that are supplements of the same angle must be congruent. This problem includes key geometry concepts and theorems suitable for students in Grades 7-9.

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