To determine the angle corresponding to the number 4 in a pie chart based on the given frequencies of a fair die, we need to follow a series of steps. Let's break it down step-by-step. ### Step 1: Understand the Data We have the following frequencies for each face of the die: - Face 1: 30 times - Face 2: 43 times - Face 3: 54 times - Face 4: 40 times - Face 5: 41 times - Face 6: 32 times ### Step 2: Calculate the Total Frequency To create a pie chart, we first need to find the total number of times the die was tossed. We do this by adding all the frequencies together: \[ \text{Total Frequency} = 30 + 43 + 54 + 40 + 41 + 32 \] Calculating this: \[ \text{Total Frequency} = 30 + 43 = 73 \] \[ 73 + 54 = 127 \] \[ 127 + 40 = 167 \] \[ 167 + 41 = 208 \] \[ 208 + 32 = 240 \] So, the total frequency is **240**. ### Step 3: Calculate the Angle for Face 4 In a pie chart, the angle corresponding to each category is calculated based on its frequency relative to the total frequency. The formula to find the angle for a specific face is: \[ \text{Angle} = \left( \frac{\text{Frequency of the face}}{\text{Total Frequency}} \right) \times 360^\circ \] For face 4, the frequency is 40. Plugging this into the formula gives: \[ \text{Angle for Face 4} = \left( \frac{40}{240} \right) \times 360^\circ \] Calculating the fraction: \[ \frac{40}{240} = \frac{1}{6} \] Now, substituting this back into the angle calculation: \[ \text{Angle for Face 4} = \left( \frac{1}{6} \right) \times 360^\circ = 60^\circ \] ### Conclusion Thus, the angle corresponding to the number 4 in the pie chart is **60°**. Therefore, the correct option is **D**. ### Step 4: Explanation of Other Options - **Option A (10°)**: This is incorrect because it significantly underestimates the frequency of face 4 relative to the total. - **Option B (16°)**: This is also incorrect as it does not accurately reflect the proportion of face 4's frequency compared to the total. - **Option C (40°)**: This option is incorrect as it suggests a higher frequency than what is represented by the actual data. ### Revision Summary - To find the angle in a pie chart, use the formula: \(\text{Angle} = \left( \frac{\text{Frequency}}{\text{Total Frequency}} \right) \times 360^\circ\). - Always sum the frequencies to get the total before calculating individual angles. - Ensure to simplify fractions where possible to make calculations easier. - Double-check calculations to avoid common pitfalls, such as miscalculating the total frequency or the angle.