The image shows a geometry problem involving angles and algebraic equations. The given diagram includes an intersection with a labeled angle of 154° and an expression (8x)° for an unknown angle.

The problem asks which equation can be used to solve for x and then requires solving for x.

Step 1: Understanding the Angle Relationship

The angles 154° and (8x)° form a linear pair, meaning they are supplementary. This means their sum equals 180°.

So, we can set up the equation:

$154 + 8x = 180$

Step 2: Solve for x

$8x = 180 - 154$

$8x = 26$

$x = \frac{26}{8} = 3.25$

Step 3: Choosing the Correct Equation

From the answer choices, the correct equation is:

$8x + 26 = 180$

Now, do you want a more detailed explanation or have any questions?

Here are some related questions:

1. What is the definition of a linear pair of angles?
2. How do we determine if two angles are supplementary?
3. What happens if two angles are complementary instead of supplementary?
4. How do we check if our solution for x is correct?
5. Can you apply this method to solve for unknown angles in a triangle?

Tip: Always check if angles are complementary (sum = 90°) or supplementary (sum = 180°) before setting up an equation.