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To solve for the missing angles \( g \), \( h \), \( k \), and \( m \), we will apply the concepts of vertically opposite angles and supplementary angles.

### Step-by-Step Solution:

1. **Vertically Opposite Angles**:
   - Angle \( h \) and the given \( 127^\circ \) are vertically opposite angles. Therefore:
     \[
     h = 127^\circ
     \]
   
2. **Supplementary Angles**:
   - \( g \) is adjacent to \( 127^\circ \) and forms a straight line with it. Since adjacent angles on a straight line sum to \( 180^\circ \), we can find \( g \) as:
     \[
     g = 180^\circ - 127^\circ = 53^\circ
     \]
   
3. **Vertically Opposite Angles (Again)**:
   - Angle \( m \) and the given \( 98^\circ \) are vertically opposite angles. Therefore:
     \[
     m = 98^\circ
     \]
   
4. **Supplementary Angles (Again)**:
   - Angle \( k \) is adjacent to \( 98^\circ \) and forms a straight line with it. So, we can find \( k \) as:
     \[
     k = 180^\circ - 98^\circ = 82^\circ
     \]

### Final Answer:
\[
g = 53^\circ, \quad h = 127^\circ, \quad k = 82^\circ, \quad m = 98^\circ
\]

Would you like further details on any of these steps or explanations? 

Here are five related questions to deepen your understanding:

1. How do vertically opposite angles relate to each other?
2. What is the sum of adjacent angles on a straight line?
3. If one angle of a straight line is \( x \), how would you find the other angle?
4. Can you explain why supplementary angles sum to \( 180^\circ \)?
5. How would the answer change if the given angles were different, say \( 120^\circ \) and \( 100^\circ \)?

**Tip**: Always remember that vertically opposite angles are equal, and angles on a straight line always sum up to \( 180^\circ \).

Find the measure of the missing angles in the given diagram where h = 127°, m = 98°.

Learn how to find the missing angles g, h, k, and m using the principles of vertically opposite angles and supplementary angles. This example involves solving for adjacent angles that sum to 180° and determining vertically opposite angle relationships. Suitable for Grades 6-8.

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