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This image presents a series of problems related to congruent and supplementary angles. Let's go over the key points for solving them:

1. **Congruent Angles** are angles that have the same measure.
2. **Supplementary Angles** are angles whose measures add up to 180°.
3. **Vertical Angles** formed by intersecting lines are always congruent.

### Breakdown of Problems

1. **Top-left:**
   - The two angles formed by the intersection are congruent. You can set the expressions equal to each other and solve for \( x \):
   \[
   (x + 1)° = (3x - 11)°
   \]

2. **Top-right:**
   - Two supplementary angles are given. Use the fact that their sum is 180°:
   \[
   (4x)° + (3x + 40)° = 180°
   \]
   Solve for \( x \).

3. **Middle-left:**
   - This involves vertical angles, which are congruent. Use:
   \[
   5x° = (3x + 50)°
   \]

4. **Middle-right:**
   - These angles are part of a linear pair, so they are supplementary. Set them equal to 180° and solve for \( x \):
   \[
   6x° + (3x)° = 180°
   \]

5. **Bottom-left:**
   - A pair of angles on a straight line are supplementary. Set them equal to 180°:
   \[
   (20x + 5)° + (24x)° = 180°
   \]

6. **Bottom-right:**
   - This is another case of vertical angles. Set the two angles equal to each other and solve for \( y \):
   \[
   5y° = (2y + 78)°
   \]

Would you like detailed solutions for any specific problems, or do you have any questions?

### Related Questions:
1. How do you know when angles are congruent or supplementary?
2. What is the process for solving linear equations when angles are involved?
3. Can angles be both congruent and supplementary at the same time? Explain.
4. How do vertical angles and corresponding angles differ?
5. What are some real-world applications of congruent and supplementary angles?

**Tip:** Always check whether the angles you're working with form a linear pair (supplementary) or vertical angles (congruent) when lines intersect!

Solve for x and y in a series of problems involving congruent and supplementary angles.

This worksheet helps solve for x and y in problems involving congruent and supplementary angles, using key geometry concepts like vertical angles, linear pairs, and angle relationships. Suitable for students in Grades 7-9.

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