Geometry homework worksheet focusing on angle bisectors with multiple problems and diagrams.

I'll solve this geometry worksheet on angle bisectors step by step.

Looking at the image, I can see it's "Practice Worksheet 1.5A - Angle Bisectors" with 5 problems. Each problem involves finding angle measures or solving for variables based on angle bisectors.

Let me solve each problem one by one:

Problem 1:
If m∠DEG = 88°, find m∠FEG.
Since EF bisects ∠DEG, it divides the angle into two equal parts.
So m∠FEG = m∠DEG ÷ 2 = 88° ÷ 2 = 44°

Problem 2:
If m∠FED = 27°, find m∠GED.
Since EF bisects ∠DEG, and we're given m∠FED = 27°, then m∠FEG must also be 27° (because the bisector creates two equal angles).
Therefore, m∠GED = m∠FED + m∠FEG = 27° + 27° = 54°

Problem 3:
If m∠DEF = 3x + 1 and m∠DEG = 5x + 19, find the value of x.
Since EF bisects ∠DEG, we know that m∠DEF = m∠FEG, and m∠DEG = m∠DEF + m∠FEG = 2 × m∠DEF.
So: 5x + 19 = 2(3x + 1)
5x + 19 = 6x + 2
19 - 2 = 6x - 5x
17 = x

Problem 4:
If m∠FEG = 5x - 3 and m∠FED = 2x + 11, find the value of x.
Since EF bisects ∠DEG, we know that m∠FEG = m∠FED.
So: 5x - 3 = 2x + 11
5x - 2x = 11 + 3
3x = 14
x = 14/3

Problem 5:
If m∠FEG = 4x - 7 and m∠FED = 2x + 11, find the m∠DEG (solve for a final answer).
Since EF bisects ∠DEG, we know that m∠FEG = m∠FED.
So: 4x - 7 = 2x + 11
4x - 2x = 11 + 7
2x = 18
x = 9

Now that we have x = 9, we can find m∠FEG = 4x - 7 = 4(9) - 7 = 36 - 7 = 29°
Since m∠DEG = m∠FEG + m∠FED = 2 × m∠FEG (because they're equal),
m∠DEG = 2 × 29° = 58°

Let me verify my answers:
- Problem 1: 44° ✓
- Problem 2: 54° ✓
- Problem 3: x = 17 ✓
- Problem 4: x = 14/3 ✓
- Problem 5: m∠DEG = 58° ✓

All solutions are complete and correct.