Math Problem Statement

answer

What is the central angle subtended by the sector which represents the votes received by Party E?

Solution

To calculate the central angle for Party E, we use the formula:

Central Angle=(Percentage of Votes100)×360\text{Central Angle} = \left(\frac{\text{Percentage of Votes}}{100}\right) \times 360^\circ

Given that Party E received 15.6% of the votes:

Central Angle=(15.6100)×360=56.16\text{Central Angle} = \left(\frac{15.6}{100}\right) \times 360^\circ = 56.16^\circ

The correct answer is 56.16°.

Would you like more explanation or details?

  1. What formula is used for calculating angles in pie charts?
  2. How does the total number of votes relate to the central angle?
  3. Can you explain the steps for deriving the central angle for any party?
  4. How would this calculation change if there were fewer divisions in the pie chart?
  5. What are some practical applications of pie charts in real-world analysis?

Tip: Always verify the total percentage sums to 100% before calculating angles!

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Math Problem Analysis

Mathematical Concepts

Geometry
Percentage Calculations
Angles in Pie Charts

Formulas

Central Angle = (Percentage of Votes / 100) × 360°

Theorems

Basic Angle-Sector Proportions in Circles

Suitable Grade Level

Grades 6-8