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.