To solve the problem of finding the amount represented by the largest sector on a pie chart, we need to follow a series of logical steps. Let's break it down step-by-step. ### Step 1: Understand the Pie Chart A pie chart represents data in a circular format, where each sector (or slice) corresponds to a proportion of the whole. The total angle in a pie chart is always 360°. In this case, we have three known angles: 45°, 90°, and 135°. ### Step 2: Calculate the Total Angle of the Known Sectors First, we need to find the total angle of the known sectors: - 45° + 90° + 135° = 270° ### Step 3: Determine the Angle of the Unknown Sector Since the total angle in a pie chart is 360°, we can find the angle of the unknown sector by subtracting the total of the known angles from 360°: - Angle of the unknown sector = 360° - 270° = 90° ### Step 4: Find the Total Value Represented by the Pie Chart We know that the smallest sector (which is 45°) represents N28.00. To find the total value represented by the pie chart, we need to determine the value per degree. First, we calculate the value per degree: - Value per degree = Amount represented by the smallest sector / Angle of the smallest sector - Value per degree = N28.00 / 45° = N0.6222 (approximately) ### Step 5: Calculate the Value of Each Sector Now that we have the value per degree, we can calculate the value of each sector: 1. **For the 45° sector:** - Value = 45° * N0.6222 = N28.00 (as expected) 2. **For the 90° sector:** - Value = 90° * N0.6222 = N56.00 3. **For the 135° sector:** - Value = 135° * N0.6222 = N84.00 4. **For the unknown sector (90°):** - Value = 90° * N0.6222 = N56.00 (as calculated above) ### Step 6: Identify the Largest Sector From our calculations, we have: - 45° sector = N28.00 - 90° sector = N56.00 - 135° sector = N84.00 - Unknown sector (90°) = N56.00 The largest sector is the one with the angle of 135°, which corresponds to N84.00. ### Step 7: Evaluate the Options Now, let's look at the options provided: - A. N96.00 - B. N84.00 - C. N48.00 - D. N42.00 The correct answer is **B. N84.00**, as it represents the value of the largest sector (135°). ### Why Other Options Are Incorrect - **A. N96.00**: This value does not correspond to any of the sectors calculated. It is higher than the maximum value we found (N84.00). - **C. N48.00**: This value does not match any of the sectors. It is also lower than the smallest sector value (N28.00). - **D. N42.00**: Similar to option C, this value does not correspond to any sector and is lower than the smallest sector value. ### Revision Summary - A pie chart's total angle is 360°, and the angles of the sectors must sum to this total. - The value represented by each sector can be calculated using the value per degree derived from the smallest sector. - The largest sector corresponds to the largest angle, which in this case is 135°. - The correct answer is B. N84.00, representing the largest sector on the pie chart.