To solve this problem, let's analyze the two diagrams provided and determine whether they are possible based on the given lines and angles.

Analysis:

1. Diagram 1:

   • There are two lines, and they appear to intersect, forming four angles.
   • Angles labeled $m$ and $90^\circ$ are given.
   • The angle adjacent to $m$ is labeled as $m$.
   • The key observation here is that angles around a point should add up to $180^\circ$.

2. Diagram 2:

   • Again, two lines intersect forming four angles.
   • Here, angles $n$ and $2n$ are provided.
   • The key observation is that these angles should also add up to $180^\circ$ if they are adjacent.

Steps:

• For Diagram 1:

  • The given angles are $m$ and $90^\circ$.
  • The adjacent angles must satisfy $m + 90^\circ = 180^\circ$.
  • This implies $m = 90^\circ$.

• For Diagram 2:

  • The given angles are $n$ and $2n$.
  • The adjacent angles must satisfy $n + 2n = 180^\circ$.
  • This implies $3n = 180^\circ$, so $n = 60^\circ$.

Conclusion:

Both diagrams satisfy the conditions necessary for the angles in them to form a valid intersection.

Answer:

• Correct answer: "Choice 1 and Choice 2."

Let me know if you want further details, explanations, or if you have more questions.

Relative Questions:

1. What is the relationship between supplementary angles?
2. How do you determine the value of unknown angles in a diagram?
3. What is the sum of the angles around a point in an intersection?
4. How can you verify if two lines are parallel based on angle measures?
5. What are vertical angles, and how do they relate to intersecting lines?

Tip:

When dealing with intersecting lines, always remember that the sum of angles around a point is $360^\circ$ and the sum of angles on a straight line is $180^\circ$.