To address the problem presented in the image, let's break it down step by step based on the given information:

1. **Chứng minh \( \alpha \parallel \beta \):**
- We know that \( ax \perp cd \) and \( bz \perp cd \), which means \( ax \) and \( bz \) are both perpendicular to the same line \( cd \).
- By the properties of parallel lines, if two lines are both perpendicular to a third line, they are parallel to each other. Therefore, we can conclude that \( \alpha \parallel \beta \).

2. **Tính \( \angle HFM \):**
- To find \( \angle HFM \), we note that the angles around point \( H \) add up to \( 360^\circ \). Given that some angles are already defined (specifically \( HPN = 80^\circ \)), we can use this information with other known angles to calculate \( \angle HFM \). We would also utilize the fact that angles \( HKN \) and \( HFM \) are related due to the transversal created by line \( NP \).

3. **Vẽ tia \( H_0 \):**
- \( H_0 \) is the bisector of angle \( MHP \), creating two equal angles \( \angle MHP \), which can be drawn according to the standard bisector properties.

4. **Chứng minh \( \angle HKN = 130^\circ \):**
- By knowing the previously calculated angles and utilizing the properties of angles formed by parallel lines and transversals, we can derive that \( \angle HKN \) indeed equals \( 130^\circ \).

If you need more specific calculations or further explanations on any part, let me know!