Worksheet: Circle Graph and Central Angle

In this worksheet, we will practice how to construct a circle graph and find the central angles of its sectors.

Q1:

The pie chart shows the favorite subjects of students in a class. Using the information given on the pie chart, determine the percentage of students who chose English.

Q2:

The results of a survey on the favourite hobbies of students are shown in the pie chart. What is the measure of the angle of the sector representing swimming?

Q3:

The given figure shows the grades of students in an exam. What is the central angle of the section that represents students who got a grade of excellent?

Q4:

Find the measures of the angles of the reading and travel sectors in this pie chart.

  • A 6 8 . 4 , 2 0 5 . 2
  • B 5 0 . 4 , 1 0 0 . 8
  • C 9 6 . 4 , 1 6 0 . 8
  • D 5 7 . 6 , 1 1 5 . 2
  • E 6 8 . 4 , 1 3 6 . 8

Q5:

James surveyed the people in his school to find their favorite sport. He displayed the data in a pie chart.

The same number of people prefer gymnastics as cross-country. What is the angle of the sector representing gymnastics?

The number of people who prefer baseball is 38. How many people prefer hockey?

How many people were surveyed in total?

Q6:

A jeweler makes a pair of earrings by cutting two 62 sectors from a silver circular disk. Determine, to the nearest milligram, how many milligrams the silver wedge for each earring weighs if the weight of the silver disk is 2.8 g.

Q7:

Hannah investigated the favorite snacks of the students in her grade and is going to display the data in a pie chart.

Snack Chips Fruit Chocolate Yogurt Nuts
Frequency 31 22 48 7 12

How many students did she survey?

To put the data in a pie chart, she needs to calculate the measure of the angle of the sector that would represent one person.

Calculate the measure of this angle.

Find the measure of the angle of the sector representing the students who prefer chocolate.

Find the measure of the angle of the smallest sector.

Q8:

Calculate the central angle of the section which shows the percentage of Italian tourists who visited a country in 2005.

  • A 1 0 8
  • B 8 6 . 4
  • C 6 1 . 2
  • D 1 0 4 . 4

Q9:

A pie chart will be used to show the number of tourists, in thousands, who visited a country in 2005. The table shows the number of tourists, but the angle of each sector of the pie chart is missing. What is the exact angle of the sector representing the French tourists?

Nationality American Egyptian Italian French Total
Number of Tourists 800 280 760 160 2,000
Angle 3 6 0
  • A 2 8 . 8
  • B 1 3 6 . 8
  • C 5 0 . 4
  • D 1 4 4
  • E 3 3 1 . 2

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