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The given image shows a right triangle where one angle is labeled as \( (5m + 5)^\circ \) and the other angle is labeled as \( (8m + 7)^\circ \). The third angle, being a right angle, is \( 90^\circ \).

In a triangle, the sum of all angles must equal \( 180^\circ \). Therefore, we can set up the following equation:

\[
(5m + 5)^\circ + (8m + 7)^\circ + 90^\circ = 180^\circ
\]

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

First, combine the terms on the left side:
\[
(5m + 5) + (8m + 7) + 90 = 180
\]

Simplify:
\[
5m + 8m + 5 + 7 + 90 = 180
\]
\[
13m + 102 = 180
\]

Subtract 102 from both sides:
\[
13m = 78
\]

Now, divide by 13:
\[
m = 6
\]

So, the value of \( m \) is \( \boxed{6} \).

Would you like more details on the steps, or do you have any further questions?

Here are 5 related questions to explore:
1. How do we know that the angles in a triangle add up to 180 degrees?
2. Can the angles of any triangle be negative? Why or why not?
3. How would the equation change if the angle sum were different, like in a quadrilateral?
4. What is the significance of a right angle in this problem?
5. How would you verify the solution by substituting \( m = 6 \) back into the angle expressions?

**Tip:** Always remember to check if your calculated angles make sense (i.e., they should all be positive and add up correctly).

Solve for the value of m. The given diagram shows a right triangle where one angle is labeled as (5m + 5)° and the other angle is labeled as (8m + 7)°. The third angle is a right angle (90°).

This problem involves solving for the variable m in a right triangle where two angles are expressed as algebraic terms (5m + 5)° and (8m + 7)°, with the third angle being a right angle (90°). Learn how to apply the angle sum property of triangles and solve the equation step by step. Suitable for students in Grades 8-10.

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