https://file.aiquickdraw.com/mathbot/file/1725997611852fanlnrvw.jpg

I can now see the image. Let's work through the problems one by one:

### Questions 1-7 (based on the diagram in the top half):
1. **Name the sides of ∠4.**
   - The sides of ∠4 are rays **DF** and **DE**.

2. **Name the vertex of ∠2.**
   - The vertex of ∠2 is point **D**.

3. **Give another name for ∠3.**
   - Another name for ∠3 is **∠CDF**.

4. **Classify ∠5.**
   - ∠5 is a **right angle** (since it is marked as 90°).

5. **Classify ∠CDE.**
   - ∠CDE is a **straight angle** (since it forms a straight line).

6. **If m∠2 = 42° and m∠1 = 117°, find m∠CDF.**
   - Since ∠1 and ∠CDF form a straight angle, \(m\angle CDF = 180^\circ - m\angle 1\).
     \[
     m\angle CDF = 180^\circ - 117^\circ = 63^\circ
     \]
     Thus, \(m\angle CDF = 63^\circ\).

7. **If m∠3 = 73°, find m∠FDE.**
   - Since ∠3 and ∠FDE form a straight line, we can find:
     \[
     m\angle FDE = 180^\circ - m\angle 3 = 180^\circ - 73^\circ = 107^\circ
     \]
     Thus, \(m\angle FDE = 107^\circ\).

### Questions 8-10 (based on the diagram in the bottom half):
8. **If m∠ZABF = (7x + 20)°, m∠FBC = (2x - 5)°, and m∠ABC = 159°, find the value of x.**
   - The sum of the angles around point **B** must equal 180°, so:
     \[
     (7x + 20) + (2x - 5) + 159 = 180
     \]
     Simplifying:
     \[
     9x + 174 = 180
     \]
     Subtract 174 from both sides:
     \[
     9x = 6
     \]
     Solving for \(x\):
     \[
     x = \frac{6}{9} = \frac{2}{3}
     \]

9. **If m∠DBC = (12x - 3)°, m∠DBE = (5x + 12)°, and m∠EBC = (3x + 13)°, find m∠EBC.**
   - The sum of the angles around point **B** should equal 180°, so:
     \[
     (12x - 3) + (5x + 12) + (3x + 13) = 180
     \]
     Simplifying:
     \[
     20x + 22 = 180
     \]
     Subtract 22 from both sides:
     \[
     20x = 158
     \]
     Solving for \(x\):
     \[
     x = \frac{158}{20} = 7.9
     \]
     Now, find \(m\angle EBC\):
     \[
     m\angle EBC = 3x + 13 = 3(7.9) + 13 = 23.7 + 13 = 36.7^\circ
     \]

10. **If m∠FBC = (10x - 9)°, m∠CBE = (4x + 15)°, find m∠FBE.**
   - The sum of the two angles must equal 180° (since they form a straight line):
     \[
     (10x - 9) + (4x + 15) = 180
     \]
     Simplifying:
     \[
     14x + 6 = 180
     \]
     Subtract 6 from both sides:
     \[
     14x = 174
     \]
     Solving for \(x\):
     \[
     x = \frac{174}{14} = 12.43
     \]
     Now, find \(m\angle FBE\):
     \[
     m\angle FBE = 180^\circ
     \]

Let me know if you'd like further details or explanations.

Here are 5 related questions to expand your understanding:
1. What is a complementary angle and how does it relate to this quiz?
2. How can we classify angles based on their measurements?
3. How would you solve for unknown angles in a triangle?
4. What are linear pairs of angles, and where do they appear in the diagrams?
5. How can bisectors be used to find unknown angle measures?

**Tip**: When solving for angles, always check if angles form a straight line (180°) or a right angle (90°) for easy calculations.

Geometry quiz on angle measures and relationships, involving angle classification, vertex identification, and solving for unknown angles using algebraic expressions.

This geometry quiz covers angle measures, relationships, and algebraic expressions. Learn how to classify angles, identify vertices, and solve for unknown angles using the angle addition postulate and bisector theorem. Suitable for students in Grades 9-10.

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