Let's analyze the given diagram and the statements to determine which one is false.

Diagram Analysis:

• The diagram shows two parallel lines $a$ and $b$ intersected by two transversals, creating various angles.
• One of the angles is labeled as $144^\circ$.

Angle Relationships:

1. Corresponding Angles: Angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
2. Alternate Interior Angles: Angles that lie between the two lines on opposite sides of the transversal. These angles are equal if the lines are parallel.
3. Supplementary Angles: Two angles that add up to $180^\circ$.

Calculations:

1. Angle $144^\circ$:

   • Since the angle is on a straight line, the adjacent angle (angle next to $144^\circ$) will be $180^\circ - 144^\circ = 36^\circ$.

2. Identifying Other Angles:

   • $\angle g$ is corresponding to the angle adjacent to $144^\circ$, so $\angle g = 36^\circ$.
   • $\angle a$ is alternate interior to $144^\circ$, so it should be $144^\circ$.
   • $\angle c$ is alternate interior to $36^\circ$, so $\angle c = 36^\circ$.
   • $\angle e$ is corresponding to $36^\circ$, so $\angle e = 36^\circ$.

Statements:

• $\angle g = 36^\circ$ (True)
• $\angle a = 36^\circ$ (False)
• $\angle c = 36^\circ$ (True)
• $\angle e = 36^\circ$ (True)

Conclusion:

The statement $\angle a = 36^\circ$ is false because $\angle a$ should be $144^\circ$.

Correct Answer:

• $\angle a = 36^\circ$ is the false statement.

Let me know if you have any questions or need further explanation.

Relative Questions:

1. What is the definition of corresponding angles?
2. How can you identify alternate interior angles?
3. What is the sum of the angles on a straight line?
4. How do parallel lines affect the angles formed by a transversal?
5. Can supplementary angles ever be equal?

Tip:

When working with parallel lines and a transversal, remember that corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary.