Proof:

To prove that if the sum of two adjacent angles is 180 degrees, then the non-common arms of the angles form a line, we will proceed with the following steps:

Step 1: Given Information

We are given two adjacent angles whose sum is 180 degrees.

Let the two angles be ∠ABC and ∠CBD, where ∠ABC and ∠CBD are adjacent angles.

Step 2: Definitions

Adjacent angles: Two angles that have a common vertex and a common side between them are called adjacent angles.

Step 3: Construction

Let AD be the common arm of the two angles ∠ABC and ∠CBD.

Step 4: Proof

Since the sum of the two adjacent angles ∠ABC and ∠CBD is 180 degrees, we can write it as:

∠ABC + ∠CBD = 180 degrees. --(1)

Now, let's assume that the non-common arms of the angles ∠ABC and ∠CBD, namely AB and CD, do not form a line.

In this case, the arms AB and CD will intersect at a point E, as shown:

```
A
\
\
E
/
/
B
```

Now, by the angle addition postulate, we can write:

∠ABC + ∠CBD = ∠ABE + ∠CBD = ∠ABE + ∠EBD. --(2)

As AB and CD do not form a line, the angles ∠ABE and ∠EBD are less than 180 degrees each. Therefore, their sum (∠ABE + ∠EBD) will be less than 180 degrees.

But from equation (1), we know that the sum of ∠ABC and ∠CBD is 180 degrees.

This contradicts equation (2), which implies that ∠ABC + ∠CBD is less than 180 degrees.

Hence, our assumption that AB and CD do not form a line is incorrect.

Step 5: Conclusion

Therefore, we can conclude that if the sum of two adjacent angles is 180 degrees, then the non-common arms of the angles form a line.

Note: The use of HTML tags such as `` for headings and key points, as well as the visual presentation of the proof, are not possible in this plain text format. However, when presenting this proof on a platform that supports HTML, the provided instructions can be followed to enhance the visual appeal of the content.