https://file.aiquickdraw.com/mathbot/file/1726844122967csxpny3k.jpg

Tell whether each of angles are complementary, supplementary, vertical, a linear pair or adjacent. Select all that apply.

In the provided image, we can see two intersecting lines, which form several angles. Specifically, angles \( \angle g \) and \( \angle m \) are labeled. Here's how to classify the relationship between these angles:

1. **Vertical Angles**: Two angles are vertical if they are opposite each other when two lines intersect. In this case, \( \angle g \) and \( \angle m \) do not appear to be directly opposite each other. Therefore, they are not vertical angles.

2. **Linear Pair**: A linear pair consists of two adjacent angles that are formed by two intersecting lines, and their sum is 180 degrees. In the image, \( \angle g \) and \( \angle m \) form a linear pair because they are adjacent and the sum of their measures is 180°, meaning they are supplementary.

3. **Supplementary Angles**: Angles are supplementary if their measures add up to 180°. Since \( \angle g \) and \( \angle m \) form a straight line (a linear pair), they are supplementary.

4. **Adjacent Angles**: Angles are adjacent if they share a common side and vertex without overlapping. \( \angle g \) and \( \angle m \) share a common side (the line between them) and a vertex. Therefore, they are adjacent.

5. **Complementary Angles**: Angles are complementary if their measures add up to 90°. Since these angles form a straight line, their sum is 180°, not 90°. Hence, they are not complementary.

### Summary:
- \( \angle g \) and \( \angle m \) are:
  - A linear pair.
  - Supplementary.
  - Adjacent.

Would you like any further clarifications or additional details?

Here are 5 questions to further expand the topic:
1. What are the key differences between supplementary and complementary angles?
2. Can two angles be both vertical and adjacent at the same time?
3. How do we calculate the measure of an angle in a linear pair if one angle is given?
4. What are some real-world applications of identifying vertical or supplementary angles?
5. How does the property of adjacent angles change in polygons with more than four sides?

**Tip:** When two lines intersect, the vertical angles formed are always congruent!

In this problem, we analyze the relationship between angles g and m formed by two intersecting lines. Learn how to classify angles as vertical, a linear pair, supplementary, or adjacent based on their position and properties. This problem is suitable for students in Grades 6-8.

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