https://file.aiquickdraw.com/mathbot/file/17262343486991cmop6kf.jpg

The image shows two intersecting lines forming two adjacent angles, labeled \( (10x - 2)^\circ \) and \( (5x + 8)^\circ \). Since these two angles are adjacent and form a straight line, they are supplementary, meaning their sum equals \(180^\circ\).

Let's set up the equation:

\[
(10x - 2) + (5x + 8) = 180
\]

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

\[
10x - 2 + 5x + 8 = 180
\]
\[
15x + 6 = 180
\]
\[
15x = 180 - 6
\]
\[
15x = 174
\]
\[
x = \frac{174}{15}
\]
\[
x = 11.6
\]

Now that we have \(x = 11.6\), we can find the actual measures of the two angles.

For the angle \( (10x - 2)^\circ \):

\[
10(11.6) - 2 = 116 - 2 = 114^\circ
\]

For the angle \( (5x + 8)^\circ \):

\[
5(11.6) + 8 = 58 + 8 = 66^\circ
\]

Thus, the two angles are \( 114^\circ \) and \( 66^\circ \), and they add up to \(180^\circ\), confirming that they are supplementary.

Would you like more details or clarifications on this? 

Here are 5 related questions:
1. What are complementary angles, and how do they differ from supplementary angles?
2. How can you determine the value of \(x\) if you are given a different pair of angles?
3. Can angles on a straight line ever be less than \(180^\circ\)?
4. How are vertical angles formed, and how are they related to each other?
5. What is the sum of the interior angles of a triangle?

**Tip:** Always check if angles are supplementary or complementary when dealing with straight lines or right angles.

Solve for x and find the angles in the diagram where two adjacent angles are represented as (10x - 2)° and (5x + 8)°, knowing they are supplementary.

Learn how to solve for x in a pair of supplementary angles, (10x - 2)° and (5x + 8)°, by setting up a linear equation. This step-by-step solution is suitable for students in Grades 8-10, covering algebraic methods and angle properties.

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