To solve the problem from the diagram, we'll address the parts step by step:

### a) Chứng minh \( ax \parallel by \)

Given that \( ax \perp m \) and \( by \perp m \), both lines \( ax \) and \( by \) are perpendicular to the same line \( m \). According to the property of parallel lines (if two lines are perpendicular to the same line, they are parallel to each other), we can conclude:

\[
ax \parallel by
\]

### b) Tính số đo \( CBx \)

Since \( BCD = 62^\circ \) and we know that \( CB \) is a transversal line intersecting the parallel lines \( ax \) and \( by \), we can apply the Alternate Interior Angles Theorem.

Thus,

\[
CBx = BCD = 62^\circ
\]

### c) Vẽ tia \( Bt \) là tia phản giác của \( CBx \)

To construct the line \( Bt \):

1. **Draw the line \( CBx \) and extend it to point \( t \)** such that \( Bt \) represents the opposite ray.
2. From point \( C \), draw a perpendicular line to line \( m \) extending downward. This line will intersect line \( by \) at point \( E \).
3. By construction, since \( CB \) is perpendicular to \( m \), and \( m \) is parallel to both \( ax \) and \( by \), it helps us confirm that \( Bt \) is the opposite ray to \( CBx \).

### Conclusion

The proofs show that \( ax \parallel by \), \( CBx = 62^\circ \), and the ray \( Bt \) serves as the opposite ray of \( CBx \). Thus, all parts are consistent with the properties of parallel lines, transversals, and angles formed.

If any further clarification or additional drawings are needed, please let me know!