https://file.aiquickdraw.com/mathbot/file/1729278991590ydaxoumh.jpg

In the image, we are asked to solve for \( k \), where the angles formed by the two intersecting lines are given as \( (9k + 6)^\circ \) and \( (4k + 5)^\circ \).

These two angles are **supplementary** because they are adjacent angles on a straight line. Supplementary angles sum up to 180°. So, we can set up the following equation:

\[
(9k + 6) + (4k + 5) = 180
\]

Now, let's solve for \( k \):

1. Combine like terms:
\[
9k + 4k + 6 + 5 = 180
\]
\[
13k + 11 = 180
\]

2. Subtract 11 from both sides:
\[
13k = 180 - 11
\]
\[
13k = 169
\]

3. Divide by 13:
\[
k = \frac{169}{13}
\]
\[
k = 13
\]

So, the value of \( k \) is \( \boxed{13} \).

Would you like more details or have any further questions?

Here are 5 related questions to expand on this problem:
1. What is the value of each angle when \( k = 13 \)?
2. What would change if the angles were complementary instead of supplementary?
3. How would you verify the result by substituting \( k = 13 \) into both angles?
4. Can this problem be generalized for any supplementary angle pair like this?
5. How would the approach change if the angles were vertically opposite?

**Tip:** When dealing with angles on a straight line, always remember that their sum is 180°, as they form supplementary angles.

Solve for the value of k when the angles formed are (9k + 6)° and (4k + 5)° as shown in the image.

Learn how to solve for k when two supplementary angles are given as (9k + 6)° and (4k + 5)°. A step-by-step guide using algebra and geometry concepts, suitable for students in Grades 6-8.

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