Mathematics
Grade 9
15 min
Circle graphs and central angles
Circle graphs and central angles
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define a circle graph and its components, including sectors and central angles.
Explain the proportional relationship between a data category's percentage and its corresponding central angle.
Calculate the measure of a central angle for a data category given its value and the total.
Determine the value or percentage of a data category from its central angle.
Construct an accurate circle graph from a given data set using a protractor.
Interpret and analyze data presented in a circle graph to answer questions.
Verify that the sum of all central angles in any circle graph is 360°.
Ever wondered how your phone's storage usage is displayed as a colorful circle? 📱 That's a circle graph, and math is the secret to making it accurate!
This tutor...
2
Key Concepts & Vocabulary
TermDefinitionExample
Circle Graph (Pie Chart)A circular statistical graphic that is divided into slices or sectors to illustrate numerical proportion. The entire circle represents 100% of the data.A chart showing that 50% of students prefer pizza, 25% prefer tacos, and 25% prefer burgers. The chart would be a circle cut into three slices.
Central AngleAn angle whose vertex is the center of a circle (point O) and whose sides are two radii of the circle. The sum of all central angles in a circle is 360°.In a pie chart, if a slice represents 25% of the data, its central angle would be 90°, because 25% of 360° is 90°.
SectorThe portion of a circle enclosed by two radii and the arc connecting them. Each 'slice' of a pie chart is a sector.The slice representing 'Rent' in a...
3
Core Formulas
Calculating Central Angle from Data
Central Angle = (\frac{\text{Part}}{\text{Whole}}) \times 360^{\circ}
Use this formula to find the angle for a sector when you know the value of the category (Part) and the total value of all categories (Whole).
Calculating Data from Central Angle
\text{Part} = (\frac{\text{Central Angle}}{360^{\circ}}) \times \text{Whole}
Use this formula to find the value of a category when you know its central angle and the total value of the data set.
The Sum of Angles Rule
\sum \text{Central Angles} = 360^{\circ}
The sum of all the central angles in any complete circle graph must equal 360°. This is a great way to check your work.
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
A monthly budget of $4,500 is displayed on a circle graph. The 'Rent' sector is 40% of the budget. The 'Food' sector has a central angle of 90°. The 'Utilities' sector represents $450. The rest is 'Savings'. What is the central angle for the 'Savings' sector?
A.36°
B.54°
C.72°
D.90°
Challenging
In a school election, the central angle for the winner was 60° larger than the angle for the runner-up. This difference in angle represented 120 votes. What was the total number of votes cast?
A.360
B.600
C.720
D.840
Challenging
In a circle graph of music preferences, the 'Rock' sector's central angle is 30% larger than the 'Pop' sector's angle. If the 'Pop' sector has a central angle of 100°, and the 'Country' sector is 54°, what is the central angle for the 'Other' category?
A.76°
B.130°
C.100°
D.56°
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free