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The problem asks for the measure of each numbered angle based on the given figure where line **FG** bisects both angles ∠CEB and ∠AED. Let's analyze the angles one by one.

### Given Information:
- Line **FG** bisects ∠CEB and ∠AED.

### Figure Setup:
1. **∠1**, **∠2**, **∠3**, etc., are labeled around the intersection of lines at point **E**.
2. **Line FG** bisects the vertical angles ∠CEB and ∠AED.
3. The choices for the measures of each angle are provided with multiple options for each numbered angle.

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### Step-by-step Angle Analysis:

#### For **m∠1** (Problem 30):
- Since **FG** bisects the angles, and from the diagram, we know that **∠1** is a smaller portion of the bisected angle **∠CEB**.
- The options are: A. 42°, B. 35°, C. 40°, D. 45°.
- Given that **∠CEB** is likely divided in half, the correct measure for **m∠1** is **35°**.
  
  **Answer: B. 35°**

#### For **m∠2** (Problem 31):
- **∠2** is vertically opposite to **∠1**, so it should have the same measure as **∠1**.
- The options are: A. 45°, B. 35°, C. 40°, D. 42°.
  
  **Answer: B. 35°**

#### For **m∠3** (Problem 32):
- **∠3** is adjacent to **∠2** and is part of the bisected angle **∠CEB**.
- Given the bisector, **∠CEB** might be a straight angle (180°), making **∠3** a large angle.
- The options are: A. 80°, B. 95°, C. 90°, D. 85°.
  
  **Answer: C. 90°**

#### For **m∠4** (Problem 33):
- **∠4** is adjacent to **∠3** and vertically opposite **∠5**, so it should have the same measure as **∠5**.
- The options are: A. 42°, B. 45°, C. 40°, D. 35°.
  
  **Answer: D. 35°**

#### For **m∠5** (Problem 34):
- **∠5** is vertically opposite to **∠4**, which we determined to be **35°**.
- The options are: A. 42°, B. 35°, C. 45°, D. 40°.
  
  **Answer: B. 35°**

#### For **m∠6** (Problem 35):
- **∠6** is vertically opposite to **∠3**, so it should also be **90°**.
- The options are: A. 90°, B. 95°, C. 80°, D. 85°.
  
  **Answer: A. 90°**

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Let me know if you need any further details! Here are 5 related questions to help you understand more:

1. What are the properties of bisected angles?
2. How can you calculate the measure of vertically opposite angles?
3. Why is the sum of adjacent angles on a straight line always 180°?
4. What happens to angles when two lines are bisected by a third line?
5. How does the concept of supplementary angles apply in this scenario?

**Tip:** When solving problems involving angle bisectors, remember that a bisector divides the angle into two equal parts.

Use the given information to find the measure of each numbered angle in the figure. Circle the correct answer. Line FG bisects ∠CEB and ∠AED. Find the measures of angles 1 through 6.

Learn how to determine the measures of angles 1 through 6 in a geometric figure where line FG bisects angles ∠CEB and ∠AED. This problem covers key geometric concepts like bisectors, vertically opposite angles, and supplementary angles.

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