https://file.aiquickdraw.com/mathbot/file/1726622276149d6cgpcki.jpg

In this image, we see a triangle with an exterior angle marked as \(107^\circ\) and an adjacent angle labeled as \(b\). The accompanying notes suggest the use of the "linear pair" concept from geometry, which states that adjacent angles formed by a straight line sum to \(180^\circ\).

To find the value of \(b\):
- The two angles, \(b\) and \(107^\circ\), form a linear pair.
- Therefore, their sum must be \(180^\circ\):
  \[
  b + 107^\circ = 180^\circ
  \]
- Solving for \(b\):
  \[
  b = 180^\circ - 107^\circ = 73^\circ
  \]

Thus, \(b = 73^\circ\).

Would you like further clarification on this or more details on linear pairs? Here are a few related questions:

1. How do exterior angles relate to interior angles of a triangle?
2. What is the sum of all interior angles of a triangle?
3. How can the concept of supplementary angles help in solving problems like this?
4. What are other ways to use algebra in geometry?
5. Can linear pairs exist outside of straight lines?

**Tip:** Always remember that a linear pair of angles will sum to \(180^\circ\), as they form a straight angle.

Find the angle b in a triangle where one of the exterior angles is 107° using the concept of linear pairs.

Learn how to solve for angle b in a triangle where the exterior angle is 107°. The problem covers the linear pair theorem, showing how adjacent angles formed by a straight line sum to 180°. Suitable for middle school students in Grades 6-8.

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