https://file.aiquickdraw.com/mathbot/file/172800861648489xzxsmc.jpg

In the image, we have two angles that are on a straight line, which means they are supplementary. Supplementary angles add up to \(180^\circ\).

The two angles given are:

\[
(5x - 6)^\circ \quad \text{and} \quad (6x + 21)^\circ
\]

Since they are supplementary, we can set up the following equation:

\[
(5x - 6) + (6x + 21) = 180
\]

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

1. Combine like terms:

\[
5x + 6x - 6 + 21 = 180
\]

This simplifies to:

\[
11x + 15 = 180
\]

2. Subtract 15 from both sides:

\[
11x = 165
\]

3. Divide both sides by 11:

\[
x = 15
\]

Thus, the value of \(x\) is \(15\).

Would you like further details or have any questions?

Here are some related questions:
1. What would happen if the angles were complementary instead of supplementary?
2. How would you verify the result using the individual angles?
3. What are the steps to solve if there were more variables involved?
4. Can you apply this concept to angles in polygons?
5. How can we generalize this solution to more than two angles?

**Tip:** Always double-check your angle relationships (supplementary, complementary, etc.) to avoid errors when setting up equations.

What is the value of x? (The image shows two angles on a straight line: (5x - 6)° and (6x + 21)°.)

Learn how to solve for x in a problem involving supplementary angles. The angles (5x - 6)° and (6x + 21)° add up to 180°. Follow this detailed step-by-step solution to understand how to find the value of x, covering key algebraic and geometric concepts.

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