4, 16, 30, 20, 10, 14 and 26 are represented on a pie chart. Find the sum of the angles of the bisectors representing all numbers equals to or greater than 16

1. Analyze the question

We are given a set of numbers: 4, 16, 30, 20, 10, 14, and 26. We need to find the sum of the angles on a pie chart that represent the numbers that are 16 or greater.

2. Explain the concept

To represent data on a pie chart, we follow these steps:

• Find the total sum of all the numbers in the data set.
• Identify the specific values that meet the condition (in this case, $\geq 16$).
• Calculate the sum of these specific values.
• Convert to degrees: Since a full circle is $360^\circ$, the angle for a specific group is calculated as: $$\text{Angle} = \left( \frac{\text{Sum of specific values}}{\text{Total sum}} \right) \times 360^\circ$$

3. Show the solution

Step 1: Find the total sum of the numbers. Total = $4 + 16 + 30 + 20 + 10 + 14 + 26$ Total = $120$

Step 2: Identify numbers $\geq 16$. The numbers in the set that are 16 or greater are: 16, 30, 20, and 26.

Step 3: Find the sum of these specific numbers. Sum of values $\geq 16 = 16 + 30 + 20 + 26$ Sum = $92$

Step 4: Calculate the corresponding angle.

Simplify the fraction: $\frac{92}{120} = \frac{92}{12} \times \frac{360}{10}$ (or simply divide 360 by 120 first) $360 \div 120 = 3$ $\text{Angle} = 92 \times 3$ $\text{Angle} = 276^\circ$

4. Identify the answer

Comparing our result to the given options, the correct value is $276^\circ$.

5. Tip

When dealing with pie chart questions, always check if the total sum is a factor of 360. If it is (like 120 is here), the calculation becomes much faster because $360/120 = 3$. You simply multiply your target sum by that constant!