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This problem involves finding the value of \( m \) using the concept of linear pairs and supplementary angles.

The given angles in the diagram are:
1. \( (5m + 100)^\circ \)
2. \( (2m + 10)^\circ \)

From the diagram, we can see that these two angles are adjacent and form a straight line (they are supplementary). Therefore, their sum must equal \( 180^\circ \).

We can set up the following equation:
\[
(5m + 100) + (2m + 10) = 180
\]

Now, let's solve for \( m \).

\[
7m + 110 = 180
\]
\[
7m = 180 - 110
\]
\[
7m = 70
\]
\[
m = \frac{70}{7} = 10
\]

Thus, the value of \( m \) is \( \boxed{10} \).

Would you like further details on this or have any questions?

Here are 5 related questions to consider:
1. What is the sum of two angles that form a linear pair?
2. How do you determine if two angles are supplementary?
3. What are the properties of vertical angles?
4. How can you use algebra to solve for unknown variables in geometry?
5. How do angles formed by parallel lines and a transversal relate to each other?

**Tip:** When working with geometry problems, always look for relationships between angles like linear pairs, vertical angles, and corresponding angles.

What is the value of m in the given geometry problem with angles (5m + 100)° and (2m + 10)° that form a straight line?

Solve the geometry problem where two angles, (5m + 100)° and (2m + 10)°, form a straight line and are supplementary. Follow the detailed step-by-step solution to find the value of m. Suitable for students in Grades 7-9.

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