Sure! Let's analyze and solve the problem related to the pie chart shown in the image.

Problem Statement:

In the given pie chart, you are asked to determine what percentage of the circle is occupied by sector $C$.

Observations from the Pie Chart:

• Sector $A$ is labeled as $60^\circ$.
• Sector $B$ is labeled as $120^\circ$.
• Sector $C$ is labeled as $x^\circ$ (we need to find the percentage corresponding to $C$).
• There is another sector $D$ labeled $80^\circ$.

Steps to Solve:

1. Sum of all angles in the pie chart: The total angle around a point in a circle is $360^\circ$.

2. Calculate the angle for sector $C$: $\text{Angle of sector } C = 360^\circ - (60^\circ + 120^\circ + 80^\circ)$ $\text{Angle of sector } C = 360^\circ - 260^\circ = 100^\circ$

3. Determine the percentage of the circle occupied by sector $C$: $\text{Percentage of sector } C = \left(\frac{100^\circ}{360^\circ}\right) \times 100\%$ $\text{Percentage of sector } C = \left(\frac{100}{360}\right) \times 100\% = \frac{100}{3.6}\% \approx 27.78\%$

Final Answer:

The percentage of the circle occupied by sector $C$ is approximately $27.78\%$.

Would you like any further details or explanations on this problem?

Here are five related questions to further your understanding:

1. How would you calculate the angle for a sector if you only know the percentage?
2. What is the relationship between the central angle and the area of a sector in a circle?
3. How can you determine the area of each sector if the total area of the circle is known?
4. What is the significance of each sector's angle in representing data in a pie chart?
5. How would the calculations change if the circle was divided into more sectors with different angles?

Tip: When dealing with pie charts, remember that the total percentage should always sum up to 100%. If the sum of given angles doesn’t add up to $360^\circ$, there might be an error in the problem.