To solve the given geometry problem, let's break it down into parts as stated in the prompts.

### a) Tính số đo góc \( BOx \)

1. **Given angles:**
- \( \angle ABO = 30^\circ \)
- \( \angle ODC = 80^\circ \)
- \( \angle BOD = 110^\circ \)

2. **Finding angle \( BOx \):**
- First, observe that \( Ox \parallel AB \) implies corresponding angles are equal when transversal \( BO \) intersects these lines.
- Thus, \( \angle BOx \) can be determined as:
- Using \( \angle ABO \):
\[
\angle BOx = \angle ABO = 30^\circ
\]

### b) Chứng minh \( Ox \parallel CD; AB \parallel CD \)

1. To show \( Ox \parallel CD \):
- Since \( BO \) is a transversal that intersects both \( Ox \) and \( CD \),
- We know \( \angle ODC = 80^\circ \) (given).
- Also, since \( \angle BOD = 110^\circ \):
- The angle \( \angle AOD \) can be calculated as:
\[
\angle AOB = \angle ODC + \angle BOD = 80^\circ + 110^\circ = 190^\circ
\]
- For angle relationships, we have that \( \angle ODC \) and \( \angle ABx \) are corresponding angles.
- Thus, if \( \angle ODC = \angle ABx = 80^\circ \):
- Therefore, \( Ox \parallel CD \).

2. To show \( AB \parallel CD \):
- Since we have \( \angle ABO = 30^\circ \) and \( \angle BOD = 110^\circ \),
- Calculate the alternate interior angle:
\[
\angle AOD = 180^\circ - \angle BOD = 180^\circ - 110^\circ = 70^\circ
\]
- Since \( \angle AOD \) and \( \angle ODC \) (which is \( 80^\circ \)) are supplementary,
- By the same reasoning that we did for \( Ox \parallel AB \),
- Therefore, \( AB \parallel CD \).

### Conclusion
- The measurement for angle \( BOx \) is \( 30^\circ \).
- We have established that \( Ox \parallel CD \) the necessary parallel relationships.