To find the value of $x$ in the given problem, we need to use the concept of angles on a straight line.

Problem Breakdown:

• The two angles shown are $27^\circ$ and $(8x - 1)^\circ$.
• Since they are on a straight line, the sum of these angles should be equal to $180^\circ$.

Step-by-Step Solution:

1. Set up the equation: $27^\circ + (8x - 1)^\circ = 180^\circ$

2. Simplify the equation: $27 + 8x - 1 = 180$ $8x + 26 = 180$

3. Solve for $x$: $8x = 180 - 26$ $8x = 154$ $x = \frac{154}{8}$ $x = 19.25$

Final Answer:

$x = 19.25$

Would you like more details on any part of this solution?

Related Questions:

1. What is the sum of angles on a straight line?
2. How do you find the angle between two intersecting lines?
3. Can the value of $x$ be negative in this context?
4. What are the other properties of angles on parallel lines?
5. How would you solve a similar problem with more than two angles?

Tip:

Always check the context of the problem when solving for angles. The sum of angles in a straight line must be $180^\circ$, which is a key property to remember.