Question

Lines e and f are parallel. The mAngle9 = 80° and mAngle5 = 55°.

Parallel lines e and f are cut by transversal c and d. All angles are described clockwise, from uppercase left. Where lines e and c intersect, the angles are: 1, 2, 4, 3. Where lines f and c intersect, the angles are 5, 6, 8, 7. Where lines e and d intersect, the angles are 9, 10, 12, 11. Where lines f and d intersect, the angles are 13, 14, 16, 15.
Which angle measures are correct? Select three options.

mAngle2 = 125°
mAngle3 = 55°
mAngle8= 55°
mAngle12 = 100°
mAngle14 = 100°Lines e and f are parallel. The mAngle9 = 80° and mAngle5 = 55°.

Parallel lines e and f are cut by transversal c and d. All angles are described clockwise, from uppercase left. Where lines e and c intersect, the angles are: 1, 2, 4, 3. Where lines f and c intersect, the angles are 5, 6, 8, 7. Where lines e and d intersect, the angles are 9, 10, 12, 11. Where lines f and d intersect, the angles are 13, 14, 16, 15.
Which angle measures are correct? Select three options.

mAngle2 = 125°
mAngle3 = 55°
mAngle8= 55°
mAngle12 = 100°
mAngle14 = 100°

Answer 1

To solve the problem, we can use the properties of angles formed by parallel lines and transversals. The angles are related to each other based on their positions (alternate interior, corresponding angles, etc.).

Given:
- \( m\angle 9 = 80° \)
- \( m\angle 5 = 55° \)

### Analyzing the Angles:
1. **Angle Relationships at Line e (where lines e and c intersect)**:
- \( m\angle 9 + m\angle 10 = 180° \) (supplementary, linear pair)
- Thus, \( m\angle 10 = 180° - 80° = 100° \)
- Since angles 1 and 2 are corresponding to angles 5 and 6 respectively:
- \( m\angle 1 = m\angle 5 = 55° \)
- \( m\angle 4 = m\angle 3 \) (alternate interior angles with angles 8 and 7), thus both equal \( m\angle 8 \), so \( m\angle 4 = m\angle 3 \)

2. **Angle Relationships at Line f (where lines f and c intersect)**:
- \( m\angle 6 + m\angle 5 = 180° \) (supplementary)
- Thus, \( m\angle 6 = 180° - 55° = 125° \)
- Angles 7 and 8 are corresponding with angles 3 and 4 respectively:
- \( m\angle 8 = 55° \) (alternate interior to angles 3)
- \( m\angle 7 = m\angle 6 = 125° \)

3. **Angle Relationships at Line e (where lines e and d intersect)**:
- At \( e \) and \( d \) intersections:
- \( m\angle 11 + m\angle 12 = 180° \)
- Since \( m\angle 10 + m\angle 12 = 180° \) and knowing \( m\angle 10 = 100° \), we find:
- \( m\angle 12 = 180° - 100° = 80° \)
- Angles 9 and 12 (both found from previous calculations) sum up with their relevant counterparts.

4. **Angle Relationships at Line f (where lines f and d intersect)**:
- For the intersection at \( f \) and \( d \):
- \( m\angle 13 + m\angle 14 = 180° \)
- \( m\angle 14 = 100° \) (directly corresponding and confirmed)
- Thus, \( m\angle 16 = m\angle 14 = 100° \)

### Conclusions:
Based on the analysis, we can summarize the measurements of the angles:
- \( m\angle 2 = 125° \) (correct from previous deduction)
- \( m\angle 3 = 55° \) (found from relationships)
- \( m\angle 8 = 55° \) (found from relationships)
- \( m\angle 12 = 100° \) (incorrect, should be 80°)
- \( m\angle 14 = 100° \) (correct)

### Correct Measures:
So the three correct angle measures are:
1. \( m\angle 2 = 125° \)
2. \( m\angle 3 = 55° \)
3. \( m\angle 14 = 100° \)

Thus, the three correct answers to select are:
**mAngle2 = 125°, mAngle3 = 55°, mAngle14 = 100°.**