https://file.aiquickdraw.com/mathbot/file/1726843461966fzqdw5ur.jpg

In the image, we have a geometric diagram with two angles formed around a right angle. The given angles are \((8m + 7)^\circ\) and \((5m + 5)^\circ\), and the right angle is \(90^\circ\).

Since the sum of angles around a point on a straight line is always \(180^\circ\), we can set up an equation by adding all the angles and equating it to \(180^\circ\):

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

Now, let's solve this equation step by step.

### Step 1: Combine like terms
\[
8m + 7 + 5m + 5 + 90 = 180
\]
\[
(8m + 5m) + (7 + 5 + 90) = 180
\]
\[
13m + 102 = 180
\]

### Step 2: Isolate \(m\)
Subtract 102 from both sides:
\[
13m = 180 - 102
\]
\[
13m = 78
\]

### Step 3: Solve for \(m\)
\[
m = \frac{78}{13} = 6
\]

Thus, the value of \(m\) is \(6\).

Let me know if you need further details or have any questions!

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Here are 5 related questions for deeper understanding:
1. How do we know the sum of angles around a point is \(180^\circ\)?
2. What is the relationship between a straight angle and supplementary angles?
3. What are the properties of right angles in geometry?
4. Can you calculate the value of each angle after substituting \(m = 6\)?
5. How would the equation change if one of the given angles was instead an obtuse angle?

**Tip:** Always check that the sum of all angles in a triangle or along a straight line adds up to \(180^\circ\) to confirm your calculations.

Solve for the value of m given two angles: (8m + 7)° and (5m + 5)°, with a third angle being a right angle.

Learn how to solve for the variable m in a geometric diagram with two angles expressed algebraically and a right angle. This problem covers key algebraic and geometric concepts, including the sum of angles in a right triangle and supplementary angles. Suitable for students in Grades 8-10.

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