To solve the problem, we need to analyze the given diagram and apply geometric principles. The angles labeled in the diagram are part of a full circle (360°). Let us proceed with the solution:

Step 1: Sum of angles in a circle

The total sum of angles in a circle is $360^\circ$. The angles in the diagram include:

• $18^\circ$,
• $x$,
• $2x$,
• $147^\circ$.

Thus, we can set up the equation: $x + 2x + 18^\circ + 147^\circ = 360^\circ.$

Step 2: Simplify the equation

Combine like terms: $3x + 165^\circ = 360^\circ.$

Step 3: Solve for $x$

Subtract $165^\circ$ from both sides: $3x = 195^\circ.$

Divide by 3: $x = 65^\circ.$

Final Answer:

The value of $x$ is: $\boxed{65^\circ}.$

Would you like a detailed breakdown of the process, or do you have any questions?

Here are five related questions to enhance understanding:

1. How do we calculate the sum of angles in a triangle versus a circle?
2. What is the role of complementary and supplementary angles in geometry?
3. How can we verify calculations involving angles in a circle?
4. What are some real-world applications of circular angle problems?
5. Can the value of $2x$ also provide additional verification of the result?

Tip: When solving geometric problems, always verify the sum of all angles to confirm consistency with the total (e.g., $360^\circ$ for a circle).