https://file.aiquickdraw.com/mathbot/file/1726102477138lt7ywhn4.jpg

To solve the given equation:

\[
(6r - 24) + (4r + 14) = 90
\]

Let's combine like terms and solve for \( r \).

### Step-by-step Solution:

1. Combine like terms:

\[
6r + 4r - 24 + 14 = 90
\]

This simplifies to:

\[
10r - 10 = 90
\]

2. Add 10 to both sides:

\[
10r = 100
\]

3. Divide both sides by 10:

\[
r = 10
\]

### Conclusion:

The value of \( r \) is \( 10 \).

Now, we can find the angle measure by substituting \( r = 10 \) back into one of the expressions. Let's substitute \( r = 10 \) into both expressions:

1. \( 6r - 24 = 6(10) - 24 = 60 - 24 = 36 \)
2. \( 4r + 14 = 4(10) + 14 = 40 + 14 = 54 \)

The measures of the two angles are 36° and 54°.

If you need further details or explanations, let me know!

### Follow-Up Questions:

1. What is the sum of the measures of the two angles?
2. How would the solution change if the equation was set to a different total value, such as 120?
3. Can you derive a formula for the measures of the angles in terms of any variable other than \( r \)?
4. What happens if the equation involved quadratic expressions instead of linear ones?
5. How would you solve this problem if it were part of a geometric figure, such as a triangle or a polygon?

### Tip:
Always double-check your work by substituting the solution back into the original equation to verify that it satisfies the given conditions.

(6r-24) + (4r+14) = 90

Solve for angle measure 1.

Learn how to solve the linear equation (6r-24) + (4r+14) = 90 with a detailed step-by-step solution. This problem covers key algebraic concepts, including combining like terms and solving linear equations. Suitable for students in Grades 6-8.

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