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### 7. Given:
- \( \overrightarrow{EF} \parallel \overrightarrow{GH} \)
- \( m \angle FGJ = 43^\circ \)
- \( m \angle HGI = x \)

**Problem: Find \( x \)**

Since \( \overrightarrow{EF} \parallel \overrightarrow{GH} \), and \( \overrightarrow{FGJ} \) and \( \overrightarrow{HGI} \) are on the transversal line:
- \( \angle FGJ \) and \( \angle HGI \) are corresponding angles.
- By the Corresponding Angles Postulate, \( m \angle FGJ = m \angle HGI \).
- Therefore, \( x = 43^\circ \).

### 8. Given:
- \( \overrightarrow{ABC} \) and \( \overrightarrow{DEF} \) are on a line, forming a linear pair.
- \( m \angle ABC = 67^\circ \)
- \( m \angle EBD = x \)

**Problem: Find \( x \)**

Since \( \overrightarrow{ABC} \) and \( \overrightarrow{DEF} \) are on a straight line, the angles \( \angle ABC \) and \( \angle EBD \) form a linear pair. Linear pairs add up to \( 180^\circ \):
- \( x + 67^\circ = 180^\circ \)
- Therefore, \( x = 180^\circ - 67^\circ = 113^\circ \).

### 9. Given:
- \( MN \) and \( RS \) intersect at point \( T \).

There isn't a specific question provided here, but if you need more details or a specific query solved, feel free to ask!

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Would you like any further details or have any additional questions? Here are 5 related questions to consider:

1. How do we determine angles in parallel lines cut by a transversal?
2. What is the significance of corresponding angles in geometry?
3. How do linear pairs differ from supplementary angles?
4. Can two non-adjacent angles form a linear pair?
5. How can you find the angle sum of any polygon?

**Tip:** When dealing with parallel lines, always look for angle relationships like corresponding, alternate interior, or same-side interior angles. These relationships often simplify the problem significantly.

Solve for angles based on parallel lines and linear pair relationships.

Learn how to solve angle problems using parallel lines and linear pairs. This solution covers key geometric concepts, including the Corresponding Angles Postulate and Linear Pair Theorem. Suitable for students in Grades 8-10.

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