A survey about the student government program at school finds of 245 students:
• 218 students like the program
• 27 students think the program is unnecessary
If a circle graph were made from this data, what would the measure of the central angle be for the group that likes the program?
Please list the steps on how to get the correct answer. I found out the percentage the amount of kids who like the program takes up, but I couldn't seem to figure out how to get the central angle.
360° ∙ 218 / 245 = 360° ∙ 0,88979596 = 320.3265456° = 320° 19´ 36´´
To find the measure of the central angle for the group that likes the program, we need to calculate the percentage of students who like the program out of the total number of students. Here are the steps to find the answer:
1. Determine the total number of students: In this case, the survey states that there are 245 students in total.
2. Calculate the number of students who like the program, which is given as 218.
3. Calculate the percentage of students who like the program: Divide the number of students who like the program by the total number of students, and then multiply by 100.
Percentage = (Number of students who like the program / Total number of students) × 100
In this case, the calculation would be: (218 / 245) × 100 = 89.02%
4. Determine the measure of the central angle: The measure of the central angle is given by the percentage calculated in the previous step. To find the angle in degrees, multiply the percentage by 360 degrees (since a circle is 360 degrees).
Central angle = Percentage × 360
In this case, the calculation would be: 89.02% × 360 = 320.47 degrees
So, the measure of the central angle for the group that likes the program is approximately 320.47 degrees.