MathsICSE Class 8 · Data Handling

Pie Charts: Central Angles, Construction and Interpretation (ICSE Class 8 Maths)

Updated 17 October 2026 · Fact-checked

In a pie chart each sector's central angle is $\frac{\text{value}}{\text{total}} \times 360^\circ$. All the angles add up to $360^\circ$. Conversely, the value of a sector is $\frac{\text{angle}}{360^\circ} \times \text{total}$.

Each angle is value ÷ total × 360°, so Cricket is 16 ÷ 40 × 360° = 144°, and all the angles add up to 360°.

Illustration drawn for QuestionBuddy.

Understand Pie Charts: Construction and Interpretation

The CISCE curriculum asks you to learn to draw and interpret simple pie charts with reasonable data numbers.

Pie chart. A circle divided into sectors whose sizes show how a total is shared. It is good for showing parts of a whole, not for tracking change.

Construction.
1. Add the values to get the total.
2. For each item compute the central angle: $\frac{item}{total} \times 36 0^{\circ}$ .
3. Check the angles add to $36 0^{\circ}$ .
4. Draw a circle and a starting radius; measure each angle with a protractor in turn.
5. Label every sector with its name (and value or percentage) and give the chart a title.

Percentages. A sector of angle $θ$ is $\frac{θ}{360} \times 100%$ of the whole. A quarter circle is $25%$ and a semicircle $50%$ .

Interpretation. Given the angles and the total, compute the number in each sector. The same angle in two pie charts of different totals represents different numbers, so compare angles only within one chart, or convert to numbers.

Missing sector. If one angle is unknown or given in terms of $x$ , use the fact that the sum is $36 0^{\circ}$ .

Why use 360? A full turn is $36 0^{\circ}$ , so the angle is simply the fraction of the circle.

Pie Charts: Construction and Interpretation: formulas to remember

Central angle: $θ = \frac{value}{total} \times 36 0^{\circ}$; For each item.
Value from angle: $value = \frac{θ}{36 0 ^{\circ}} \times total$; Interpretation.
Sum of angles: $\sum θ = 36 0^{\circ}$; Checking step.

How to solve Pie Charts: Construction and Interpretation questions

Find the fraction of the whole for each item, convert to an angle, and check the total.

1Find the total of all the items.
2Compute $\frac{item}{total} \times 36 0^{\circ}$ for each.
3Check the angles sum to $36 0^{\circ}$ .
4Draw the sectors in order with a protractor and label them.
5For interpretation, reverse the calculation using the total.

Pie Charts: Construction and Interpretation in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Monthly budget

Suppose a family spends Rs 24,000 in a month: food Rs 8,000, rent Rs 6,000, education Rs 4,000, savings Rs 3,000 and others Rs 3,000.

Find the central angle for each item.

Try it first, then show the solutionSolution

Food $\frac{8000}{24000} \times 360 = 12 0^{\circ}$ ; rent $9 0^{\circ}$ ; education $6 0^{\circ}$ .
Savings $4 5^{\circ}$ ; others $4 5^{\circ}$ . Sum $= 36 0^{\circ}$ .

Answer: $12 0^{\circ}, 9 0^{\circ}, 6 0^{\circ}, 4 5^{\circ}, 4 5^{\circ}$ .

Memory hook: Fraction of the whole, times a full turn.

Tricks to remember Pie Charts: Construction and Interpretation

Short memory aids. Say each one aloud once, then use it on a question the same day.

Quarter and half
90 degrees is 25 percent and 180 degrees is 50 percent; use them as checks.
Use it when: Reasonableness.
Same angle, different totals
Equal angles in charts of different totals mean different numbers.
Use it when: Comparing charts.

Pie Charts: Construction and Interpretation: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Angle for a quarter · 1 mark · MCQBoard level

The central angle of a sector that is 25% of a pie chart is:
(a) $2 5^{\circ}$ (b) $9 0^{\circ}$ (c) $4 5^{\circ}$ (d) $18 0^{\circ}$

Try it first, then show the solutionSolution

$25% \times 360 = 90$ .

Answer: (b)

Example 2: Constructing the angles · 3 marks · Short answerBoard level

A family spends Rs 24,000 in a month: food 8,000, rent 6,000, education 4,000, savings 3,000, others 3,000. Find the central angle of each sector.

Try it first, then show the solutionSolution

Food $= \frac{8000}{24000} \times 360 = 12 0^{\circ}$ .
Rent $= 9 0^{\circ}$ ; education $= 6 0^{\circ}$ .
Savings $= 4 5^{\circ}$ ; others $= 4 5^{\circ}$ . Sum $= 36 0^{\circ}$ .

Answer: $12 0^{\circ}, 9 0^{\circ}, 6 0^{\circ}, 4 5^{\circ}, 4 5^{\circ}$

Example 3: Numbers from angles · 3 marks · Short answerHarder board level

A pie chart for 600 students shows how they travel: bus $15 0^{\circ}$ , cycle $9 0^{\circ}$ , walk $7 2^{\circ}$ , car $4 8^{\circ}$ . Find the number of students in each group.

Try it first, then show the solutionSolution

Check: $150 + 90 + 72 + 48 = 360$ .
Bus $\frac{150}{360} \times 600 = 250$ ; cycle $150$ .
Walk $120$ ; car $80$ . Total $250 + 150 + 120 + 80 = 600$ .

Answer: 250, 150, 120, 80

Example 4: From frequencies to angles · 4 marks · Short answerHarder board level

In a class of 72 students the favourite colours are: red 18, blue 24, green 12, yellow 18. Find the angle of each sector and the percentage who like blue.

Try it first, then show the solutionSolution

One student $= \frac{360}{72} = 5^{\circ}$ .
Red $9 0^{\circ}$ , blue $12 0^{\circ}$ , green $6 0^{\circ}$ , yellow $9 0^{\circ}$ (sum $36 0^{\circ}$ ).
Blue $= \frac{24}{72} \times 100 = 33 \frac{1}{3} %$ .

Answer: $9 0^{\circ}, 12 0^{\circ}, 6 0^{\circ}, 9 0^{\circ}$ ; $33 \frac{1}{3} %$

Example 5: Finding a missing sector · 4 marks · Long answerHOTS / competency

A pie chart for 4,500 kg of grain has sectors: wheat $10 0^{\circ}$ , rice $8 0^{\circ}$ , pulses $(2 x)^{\circ}$ and millets $x^{\circ}$ . Find $x$ and the quantity of each grain.

Try it first, then show the solutionSolution

$100 + 80 + 2 x + x = 360 \Rightarrow 3 x = 180 \Rightarrow x = 60$ .
Pulses $12 0^{\circ}$ , millets $6 0^{\circ}$ .
Wheat $\frac{100}{360} \times 4500 = 1250$ kg; rice $1000$ kg; pulses $1500$ kg; millets $750$ kg.
Check: $1250 + 1000 + 1500 + 750 = 4500$ .

Answer: x = 60; 1250, 1000, 1500, 750 kg

Where students lose marks in Pie Charts: Construction and Interpretation

The slips examiners see most often, and what to write instead.

Mistake: Dividing by the largest value instead of the total
The fraction is item over total.
Wrong working
Angle for rent $= \frac{6000}{8000} \times 360$ .
Right working
$\frac{6000}{24000} \times 360 = 9 0^{\circ}$ .
Do this: Add all values first.
Usually costs: All angles.
Mistake: Not checking that angles sum to 360
A rounding or arithmetic slip leaves a gap in the circle.
Wrong working
Angles: $120, 90, 60, 45, 40$ .
Right working
$120 + 90 + 60 + 45 + 45 = 360$ .
Do this: Add the angles before drawing.
Usually costs: Accuracy marks.

Exam tips

Write a column for total, fraction and angle.
Label every sector with its name and value.
Use a sharp pencil and measure the angles carefully.

Practice questions on Pie Charts: Construction and Interpretation

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
The sum of all the central angles of a pie chart is:
(a) $18 0^{\circ}$ (b) $27 0^{\circ}$ (c) $36 0^{\circ}$ (d) $9 0^{\circ}$
Hint
A full circle.
Answer
(c)
Q2 · 2 marks · Short answerBoard level
In a survey of 180 people, 45 prefer tea. Find the central angle for tea in a pie chart.
Hint
Fraction of 360.
Answer
$\frac{45}{180} \times 360 = 9 0^{\circ}$ .
Q3 · 3 marks · Short answerHarder board level
A pie chart of 800 people has a sector of $5 4^{\circ}$ . How many people does it represent?
Hint
Value = angle/360 x total.
Answer
$\frac{54}{360} \times 800 = 120$ people.
Q4 · 3 marks · Short answerHarder board level
In a group of 120 people, 50 speak Hindi, 30 English, 20 Bengali and 20 other languages. Find the angle for each sector.
Hint
One person = 3 degrees.
Answer
One person $= 3^{\circ}$ : Hindi $15 0^{\circ}$ , English $9 0^{\circ}$ , Bengali $6 0^{\circ}$ , others $6 0^{\circ}$ (sum $36 0^{\circ}$ ).
Q5 · 4 marks · Long answerHOTS / competency
Pie chart A (total 400 people) has a sector of $9 0^{\circ}$ . Pie chart B (total 1200 people) has a sector of $6 0^{\circ}$ . Which sector represents more people, and by how many? Why can angles alone mislead?
Hint
Convert both to numbers.
Answer
A: $\frac{90}{360} \times 400 = 100$ . B: $\frac{60}{360} \times 1200 = 200$ . B's sector has $100$ more people even though its angle is smaller. Angles show shares of different totals, not equal numbers.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Central angle formula?Show answer
value/total x 360.
2.Angle for 50 percent?Show answer
180 degrees.
3.Sum of angles in a pie chart?Show answer
360 degrees.
4.Value of a sector of angle 72 degrees in a total of 500?Show answer
100.

Pie Charts: Construction and Interpretation: frequently asked questions

When should I use a pie chart?

To show how a whole is divided into parts.

Can two pie charts of different totals be compared by angle?

Only for shares, not for actual numbers.