Reading Pie Charts

Read a pie chart as parts of a whole: turn the angle of a sector into a fraction, a percentage or an amount, find the whole from one sector, find a missing angle, and compare two pie charts.

Before you start

The angles at a point add up to $360^\circ$ , so the angles at the centre of a circle add up to $360^\circ$ .
A fraction of a quantity: $\frac{3}{10}$ of $40 = \frac{3}{10} \times 40 = 12$ . A fraction as a percentage: $\frac{3}{10} \times 100\% = 30\%$ .
An equation such as $6x + 120 = 360$ is solved by taking 120 from both sides, $6x = 240$ , and then dividing both sides by 6, $x = 40$ .

What a Pie Chart Shows

A pie chart is a circle divided into sectors, one for each category of the data. The whole circle stands for the whole of the data: all the students asked, all the money spent, all the cups sold.

The size of each sector is set by its angle at the centre. The bigger a category's share of the whole, the bigger its angle. The angles at the centre add up to $360^\circ$ , so the whole circle, $360^\circ$ , stands for the total, which is $100\%$ of the data.

A pie chart shows at a glance how a whole is shared: which category is the largest part and which is the smallest. To find exact fractions, percentages and amounts, we use the angles.

The angle of a sector

The angle of a sector is proportional to the quantity it stands for:

$\frac{\text{angle of the sector}}{360^\circ} = \frac{\text{quantity in the sector}}{\text{total quantity}}$

The angles of all the sectors add up to $360^\circ$ , and their percentages add up to $100\%$ .

Example 1: Reading a pie chart

The pie chart shows how 40 students travel to school.

(a) Which way of travelling is the most common?

(b) What percentage of the students take the bus?

(d) How many students travel by car?

Solution

(a) The Bus sector has the largest angle, $180^\circ$ , so the bus is the most common way.

(b) Percentage $= \frac{180^\circ}{360^\circ} \times 100\% = 50\%$ . The Bus sector is half of the circle.

(d) The Car sector is $\frac{72^\circ}{360^\circ} = \frac{1}{5}$ of the circle, so it stands for $\frac{1}{5}$ of the 40 students.

Number $= \frac{1}{5} \times 40 = 8$

Check: $180^\circ + 108^\circ + 72^\circ = 360^\circ$ .

(a) The bus. (b) $50\%$ of the students take the bus. (c) $\frac{3}{10}$ of the students walk. (d) 8 students travel by car.

Fractions and Percentages from Angles, and Back

A sector of $a^\circ$ is $\frac{a}{360}$ of the whole circle, so it stands for $\frac{a}{360}$ of the total. Multiply that fraction by $100\%$ to write it as a percentage.

Going back, a percentage of the whole is the same percentage of $360^\circ$ . Since $100\%$ is $360^\circ$ , $1\%$ is $3.6^\circ$ ; so $10\%$ is $36^\circ$ , $25\%$ is $90^\circ$ and $50\%$ is $180^\circ$ .

Fraction, percentage and angle

Fraction of the whole $= \frac{\text{angle of the sector}}{360^\circ}$

Percentage of the whole $= \frac{\text{angle of the sector}}{360^\circ} \times 100\%$

Angle of the sector $= \frac{\text{percentage}}{100\%} \times 360^\circ$

Example 2: Fractions and percentages from angles

The pie chart shows the books borrowed from a school library in one week, by type.

(a) What fraction of the books borrowed were comics?

(b) What percentage of the books borrowed were fiction?

Solution

(a) Fraction $= \frac{72^\circ}{360^\circ} = \frac{1}{5}$ (dividing 72 and 360 by 72).

(b) Percentage $= \frac{162^\circ}{360^\circ} \times 100\% = 45\%$ .

The same working for every sector gives the whole table. The percentages add up to $100\%$ , as they must.

Type	Angle	Fraction	Percentage
Fiction	$162^\circ$	$\frac{9}{20}$	$45\%$
Non-fiction	$81^\circ$	$\frac{9}{40}$	$22.5\%$
Comics	$72^\circ$	$\frac{1}{5}$	$20\%$
Magazines	$45^\circ$	$\frac{1}{8}$	$12.5\%$
Total	$360^\circ$	$1$	$100\%$

(a) $\frac{1}{5}$ of the books were comics. (b) $45\%$ were fiction. (c) $22.5\%$ were non-fiction.

Example 3: From a percentage to an angle

The pie chart shows how a household uses its monthly income of $4800.

(a) Calculate the angle of the Food sector.

(b) Calculate the angle of the Transport sector.

Solution

(a) Angle $= \frac{25\%}{100\%} \times 360^\circ = 90^\circ$ . A quarter of the income is a quarter of the circle.

(b) Angle $= \frac{15\%}{100\%} \times 360^\circ = 54^\circ$ (or $15 \times 3.6^\circ = 54^\circ$ ).

Amount saved $= \frac{20}{100} \times 4800 = 960$ , so the household saves $960.

(a) $90^\circ$ (b) $54^\circ$ (c) The household saves $960 a month.

Finding an Amount from an Angle

When the total is known, each sector's share of $360^\circ$ is its share of the total. So we find the fraction $\frac{\text{angle}}{360^\circ}$ and take that fraction of the total.

A sector of $72^\circ$ does not stand for 72 students. The angle tells us the fraction of the whole; the total tells us how many that is.

An amount from an angle

Quantity in a sector $= \frac{\text{angle of the sector}}{360^\circ} \times \text{total quantity}$

The difference between two sectors $= \frac{\text{difference between their angles}}{360^\circ} \times \text{total quantity}$

Example 4: The number of students in a sector

Mr Tan asked 60 Secondary 1 students which CCA they would most like to join. The pie chart shows the results.

(a) How many students chose Basketball?

(b) How many more students chose Badminton than Choir?

Solution

(a) Basketball is $\frac{72^\circ}{360^\circ}$ of the 60 students.

Number $= \frac{72^\circ}{360^\circ} \times 60 = 12$

(b) The difference between the angles is $96^\circ - 54^\circ = 42^\circ$ .

Difference $= \frac{42^\circ}{360^\circ} \times 60 = 7$

Check: Badminton $\frac{96}{360} \times 60 = 16$ and Choir $\frac{54}{360} \times 60 = 9$ ; $16 - 9 = 7$ .

Number $= \frac{252^\circ}{360^\circ} \times 60 = 42$

(a) 12 students chose Basketball. (b) 7 more students chose Badminton than Choir. (c) 42 students did not choose Choir or Scouts.

Finding the Whole from One Sector

Sometimes the total is not given, but we are told what one sector stands for. Since the angle is proportional to the quantity, we can scale up from that sector to the whole circle.

If $45^\circ$ stands for 30 students, then $360^\circ$ , which is $\frac{360}{45} = 8$ times as large, stands for $8 \times 30 = 240$ students. A check: the whole must be more than any one part.

The whole from one sector

If a sector of $a^\circ$ stands for a quantity $q$ , then

total quantity $= \frac{360^\circ}{a^\circ} \times q$ , and a sector of $b^\circ$ stands for $\frac{b^\circ}{a^\circ} \times q$ .

If a sector is $p\%$ of the whole and stands for $q$ , then the total is $\frac{100}{p} \times q$ .

Example 5: The whole from one sector

Every Secondary 1 student of a school was asked how he or she spends most of recess. The pie chart shows the answers. The Library sector stands for 30 students.

(a) How many Secondary 1 students are there in the school?

(b) How many of them spend most of recess chatting?

Solution

(a) $45^\circ$ stands for 30 students, and the whole circle is $360^\circ$ .

Total $= \frac{360^\circ}{45^\circ} \times 30 = 8 \times 30 = 240$

(b) The Chatting sector is $120^\circ$ , compared with $45^\circ$ for 30 students.

Number $= \frac{120^\circ}{45^\circ} \times 30 = 80$

Check with the total: $\frac{120^\circ}{360^\circ} \times 240 = 80$ .

(a) There are 240 Secondary 1 students. (b) 80 of them spend most of recess chatting.

Example 6: The whole from a percentage

Hui Min asked some students to name their favourite kind of film. The pie chart shows her results. 27 students chose comedy.

(a) How many students did Hui Min ask?

(b) How many students chose animation?

Solution

(a) $30\%$ stands for 27 students.

Total $= \frac{100}{30} \times 27 = 90$

(b) Number $= \frac{20}{100} \times 90 = 18$

Check with the numbers: $\frac{27}{90} \times 360^\circ = 108^\circ$ .

(a) Hui Min asked 90 students. (b) 18 students chose animation. (c) The Comedy sector is $108^\circ$ .

Finding a Missing Angle

The angles at the centre add up to $360^\circ$ . So if every angle but one is known, the missing angle is $360^\circ$ minus the sum of the others. When a question asks you to calculate an angle, calculate it: do not measure it or judge it by eye.

When the angles are given in terms of an unknown, such as $2x^\circ$ and $(x + 20)^\circ$ , add them all, set the sum equal to $360$ , and solve the equation. When some angles are given in a ratio, they share what is left of $360^\circ$ in that ratio. For example, if the other sectors add up to $240^\circ$ , then $120^\circ$ is left; for two sectors in the ratio $1 : 2$ that is $1 + 2 = 3$ parts of $120^\circ \div 3 = 40^\circ$ , so the two angles are $40^\circ$ and $2 \times 40^\circ = 80^\circ$ .

A missing angle

Missing angle $= 360^\circ -$ (the sum of the other angles)

Angles in terms of $x$ : the sum of all the angles $= 360^\circ$ ; solve for $x$ , then work out each angle.

Example 7: A missing angle

A bubble tea stall sold 180 cups on Saturday. The pie chart shows the flavours sold.

(a) Calculate the value of $x$ .

(b) How many cups of taro bubble tea were sold?

Solution

(a) The angles add up to $360^\circ$ .

$x = 360 - (126 + 104 + 58) = 360 - 288 = 72$

(b) Number $= \frac{72^\circ}{360^\circ} \times 180 = 36$

(a) $x = 72$ (b) 36 cups of taro bubble tea were sold.

Example 8: Angles in terms of $x$

The pie chart shows how Mrs Goh's family spends $4500 a month.

(a) Find the value of $x$ .

(b) How much does the family spend on housing?

Solution

(a) The angles add up to $360^\circ$ :

$2x + 3x + (x + 20) + 100 = 360$

$6x + 120 = 360$ (collecting like terms)

$6x = 240$ (taking 120 from both sides)

$x = 40$ (dividing both sides by 6)

Check: the angles are $80^\circ$ , $120^\circ$ , $60^\circ$ and $100^\circ$ , and $80 + 120 + 60 + 100 = 360$ .

(b) The Housing sector is $3x^\circ = 3 \times 40^\circ = 120^\circ$ .

Amount $= \frac{120^\circ}{360^\circ} \times 4500 = 1500$ , so the family spends $1500 on housing.

(a) $x = 40$ (b) The family spends $1500 a month on housing.

Comparing Two Pie Charts

A pie chart shows fractions of its own total, not amounts. A bigger angle means a bigger fraction of that whole. It need not mean a bigger number, because another pie chart may stand for a much larger or smaller total.

So when two pie charts have different totals, equal angles mean equal fractions, not equal numbers. To compare the numbers, work out each one from its own total.

Equal angles need not mean equal numbers

A $90^\circ$ sector is a quarter of its whole. A quarter of 40 students is 10 students; a quarter of 400 students is 100 students.

Example 9: Two schools

The pie charts show how the students of School P (720 students) and School Q (1080 students) travel to school.

(a) The MRT sectors of the two pie charts are equal. Do the same number of students take the MRT in the two schools?

(b) Ravi says, "More students take the bus in School P than in School Q, because the Bus sector of School P is larger." Is he right? Explain.

Solution

(a) School P: $\frac{108^\circ}{360^\circ} \times 720 = 216$ students.

School Q: $\frac{108^\circ}{360^\circ} \times 1080 = 324$ students.

The equal sectors mean the same fraction, $\frac{108}{360} = \frac{3}{10}$ , of each school takes the MRT. School Q has more students, so $\frac{3}{10}$ of it is more.

(b) School P: $\frac{135^\circ}{360^\circ} \times 720 = 270$ students take the bus.

School Q: $\frac{120^\circ}{360^\circ} \times 1080 = 360$ students take the bus.

More students take the bus in School Q. What the larger sector does show is that a larger fraction of School P takes the bus: $\frac{135}{360} = 37.5\%$ against $\frac{120}{360} = 33\frac{1}{3}\%$ .

Number of students
Way of travelling	School P	School Q
Bus	270	360
MRT	216	324
Walk	144	180
Car	90	216
Total	720	1080

(a) No: 216 students take the MRT in School P and 324 in School Q. (b) Ravi is wrong: 270 students take the bus in School P and 360 in School Q. The larger sector only means a larger fraction of School P takes the bus.

Common mistakes

Taking the angle as the amount. A $72^\circ$ sector of a pie chart of 60 students stands for $\frac{72}{360} \times 60 = 12$ students, not 72.
Dividing by 100 in place of 360. The fraction is $\frac{\text{angle}}{360^\circ}$ , because the whole circle is $360^\circ$ . In the same way, $20\%$ of a pie chart is $72^\circ$ , not $20^\circ$ .
Turning the fraction upside down when finding the whole. If $45^\circ$ stands for 30, the whole is $\frac{360}{45} \times 30 = 240$ , not $\frac{45}{360} \times 30$ . The whole must be more than any one part.
Leaving out a sector when taking the known angles from $360^\circ$ , or judging a missing angle by eye. Add all the angles at the end: they must come to $360^\circ$ .
Stopping at $x$ . When the question asks for a sector's angle or amount, put the value of $x$ back into $3x$ or $(x + 20)$ .
Comparing sectors of two pie charts with different totals as if they were numbers. Equal angles mean equal fractions; the numbers depend on each total as well.

Practice

The questions get harder as you go. Try each one before you open its solution.

Practice 1: Siti's day

The pie chart shows how Siti spends the 24 hours of a school day.

(a) What fraction of the day does Siti spend sleeping?

(b) What percentage of the day does she spend on homework?

ShowHide solution

(a) Fraction $= \frac{120^\circ}{360^\circ} = \frac{1}{3}$

(b) Percentage $= \frac{45^\circ}{360^\circ} \times 100\% = 12.5\%$

(a) $\frac{1}{3}$ of the day (b) $12.5\%$ (c) 7 hours

Practice 2: Percentages and angles

(a) Mei Ling says that a sector standing for $20\%$ of a pie chart has an angle of $20^\circ$ . Explain her mistake and find the correct angle.

(b) What percentage of a pie chart is a sector of $126^\circ$ ?

ShowHide solution

(a) The whole circle is $360^\circ$ , not $100^\circ$ , so $20\%$ is $20\%$ of $360^\circ$ .

Angle $= \frac{20\%}{100\%} \times 360^\circ = 72^\circ$

(b) Percentage $= \frac{126^\circ}{360^\circ} \times 100\% = 35\%$

$x = 36$ (dividing both sides by 3)

(a) $20\%$ is $72^\circ$ , because the whole circle is $360^\circ$ . (b) $35\%$ (c) $x = 36$

Practice 3: Saturday afternoons

The students of a school were asked how they spend most of their Saturday afternoon. The pie chart shows the results.

(a) Find the value of $x$ .

(b) Calculate the angle of the Sports sector.

ShowHide solution

(a) The percentages add up to $100\%$ .

$x = 100 - (35 + 15 + 25 + 15) = 100 - 90 = 10$

(b) Angle $= \frac{35\%}{100\%} \times 360^\circ = 126^\circ$

(a) $x = 10$ (b) $126^\circ$ (c) 36 students spend most of the afternoon reading.

Practice 4: Favourite subjects

90 students were asked to name their favourite subject. The pie chart shows the results.

(a) How many students chose Maths?

(b) How many more students chose Science than Music?

ShowHide solution

(a) Number $= \frac{72^\circ}{360^\circ} \times 90 = 18$

(b) The difference between the angles is $100^\circ - 40^\circ = 60^\circ$ .

Difference $= \frac{60^\circ}{360^\circ} \times 90 = 15$

Check: Science $\frac{100}{360} \times 90 = 25$ , Music $\frac{40}{360} \times 90 = 10$ , and $25 - 10 = 15$ .

(a) 18 students (b) 15 more students (c) $\frac{7}{30}$

Practice 5: A family's spending

The pie chart shows how Mei Ling's family spends $3600 a month.

(a) How much does the family spend on food?

(b) How much more does it spend on housing than on transport?

ShowHide solution

(a) Amount $= \frac{100^\circ}{360^\circ} \times 3600 = 1000$ , so the family spends $1000 on food.

(b) The difference between the angles is $140^\circ - 50^\circ = 90^\circ$ .

Difference $= \frac{90^\circ}{360^\circ} \times 3600 = 900$ , so it spends $900 more.

Check: housing $\frac{140}{360} \times 3600 = 1400$ , transport $\frac{50}{360} \times 3600 = 500$ , and $1400 - 500 = 900$ .

(a) $1000 (b) $900 more on housing than on transport

Practice 6: Ali's pocket money

The pie chart shows how Ali used his pocket money last month. He spent $45 on food.

(a) How much pocket money did Ali have last month?

(b) How much did he save?

ShowHide solution

(a) $135^\circ$ stands for $45, and the whole circle is $360^\circ$ .

Total $= \frac{360^\circ}{135^\circ} \times 45 = 120$ , so Ali had $120.

(b) Savings $= \frac{105^\circ}{135^\circ} \times 45 = 35$ , so he saved $35.

Check with the total: $\frac{105^\circ}{360^\circ} \times 120 = 35$ .

(a) $120 (b) $35

Practice 7: Sports Day

Each of 180 Secondary 1 students took part in one event on Sports Day. The pie chart shows the events.

(a) Calculate the value of $x$ .

(b) How many students took part in the relay?

ShowHide solution

(a) The angles add up to $360^\circ$ .

$x = 360 - (88 + 64 + 52 + 60) = 360 - 264 = 96$

(b) Number $= \frac{96^\circ}{360^\circ} \times 180 = 48$

(a) $x = 96$ (b) 48 students (c) The relay

Practice 8: A level outing

240 Secondary 1 students voted for the place of a level outing. The pie chart shows the votes.

(a) Find the value of $x$ .

(b) How many students voted for the zoo?

ShowHide solution

(a) The angles add up to $360^\circ$ :

$3x + 2x + (x + 24) + x = 360$

$7x + 24 = 360$

$7x = 336$

$x = 48$

Check: the angles are $144^\circ$ , $96^\circ$ , $72^\circ$ and $48^\circ$ , and $144 + 96 + 72 + 48 = 360$ .

(b) The Zoo sector is $3 \times 48^\circ = 144^\circ$ .

Number $= \frac{144^\circ}{360^\circ} \times 240 = 96$

(c) The Gardens by the Bay sector is $48^\circ + 24^\circ = 72^\circ$ , so the difference is $144^\circ - 72^\circ = 72^\circ$ .

Difference $= \frac{72^\circ}{360^\circ} \times 240 = 48$

(a) $x = 48$ (b) 96 students (c) 48 more students

Practice 9: The whole from a difference

The pie chart shows the CCAs of the Secondary 1 students of a school. 24 more students are in the Choir than in Dance.

(a) How many Secondary 1 students are there?

(b) How many of them play basketball?

ShowHide solution

(a) The difference between the Choir and Dance sectors is $80^\circ - 50^\circ = 30^\circ$ , and it stands for 24 students.

Total $= \frac{360^\circ}{30^\circ} \times 24 = 12 \times 24 = 288$

(b) Number $= \frac{110^\circ}{360^\circ} \times 288 = 88$

Check: Choir $\frac{80}{360} \times 288 = 64$ and Dance $\frac{50}{360} \times 288 = 40$ ; $64 - 40 = 24$ .

(a) 288 students (b) 88 students play basketball.

Practice 10: Angles in a ratio

A hawker stall sold 450 plates of food on Sunday. The pie chart shows the dishes. The angles of the Chicken rice, Duck rice and Char siew rice sectors are in the ratio $2 : 3 : 4$ .

(a) Calculate the angle of each of the three rice sectors.

(b) How many plates of char siew rice were sold?

ShowHide solution

(a) The three rice sectors together are $360^\circ - 108^\circ = 252^\circ$ .

They share $252^\circ$ in the ratio $2 : 3 : 4$ , which is $2 + 3 + 4 = 9$ parts.

One part $= 252^\circ \div 9 = 28^\circ$

Chicken rice $= 2 \times 28^\circ = 56^\circ$ , Duck rice $= 3 \times 28^\circ = 84^\circ$ , Char siew rice $= 4 \times 28^\circ = 112^\circ$ .

Check: $56 + 84 + 112 + 108 = 360$ .

(b) Number $= \frac{112^\circ}{360^\circ} \times 450 = 140$

(a) Chicken rice $56^\circ$ , Duck rice $84^\circ$ , Char siew rice $112^\circ$ (b) 140 plates

Practice 11: Drinks at the canteen

Some students were asked to name their favourite drink at the school canteen. The pie chart shows the results. 36 students chose lime juice.

(a) How many students were asked?

(b) Calculate the angle of the Lime juice sector.

ShowHide solution

(a) Lime juice is $30\%$ of the whole, and $30\%$ stands for 36 students.

Total $= \frac{100}{30} \times 36 = 120$

(b) Angle $= \frac{30\%}{100\%} \times 360^\circ = 108^\circ$

Number $= \frac{60^\circ}{360^\circ} \times 120 = 20$

Check: soya bean milk $\frac{126}{360} \times 120 = 42$ , lime juice 36, sugar cane juice 20, barley $\frac{66}{360} \times 120 = 22$ ; $42 + 36 + 20 + 22 = 120$ .

(a) 120 students (b) $108^\circ$ (c) 20 students

Practice 12: Two pie charts of pocket money

Siti has $120 of pocket money a month and Mei Ling has $180. The pie charts show how each of them uses it.

(a) Their Food sectors are both $144^\circ$ . Ali says they spend the same amount on food. Is he right? Explain.

(b) Siti's Savings sector is larger than Mei Ling's. Who saves more money, and how much more?

ShowHide solution

(a) Siti: $\frac{144^\circ}{360^\circ} \times 120 = 48$ , so she spends $48 on food.

Mei Ling: $\frac{144^\circ}{360^\circ} \times 180 = 72$ , so she spends $72 on food.

The equal sectors mean they spend the same fraction, $\frac{144}{360} = \frac{2}{5}$ , of their pocket money on food, but Mei Ling has more pocket money.

(b) Siti: $\frac{108^\circ}{360^\circ} \times 120 = 36$ , so she saves $36.

Mei Ling: $\frac{96^\circ}{360^\circ} \times 180 = 48$ , so she saves $48.

Mei Ling saves more: $48 - 36 = 12$ , so she saves $12 more.

(c) Siti saves $\frac{108}{360} = \frac{3}{10} = \frac{9}{30}$ ; Mei Ling saves $\frac{96}{360} = \frac{4}{15} = \frac{8}{30}$ .

Since $\frac{9}{30} > \frac{8}{30}$ , Siti saves the greater fraction. That is what her larger sector shows.

(a) No: Siti spends $48 and Mei Ling $72 on food. (b) Mei Ling saves $12 more. (c) Siti saves the greater fraction.

Key Points

A pie chart shows how a whole is divided into parts. Each part is a sector; its size is set by its angle at the centre.
The whole circle, $360^\circ$ , stands for the total; the angles add up to $360^\circ$ and the percentages to $100\%$ .
Fraction $= \frac{\text{angle}}{360^\circ}$ ; percentage $= \frac{\text{angle}}{360^\circ} \times 100\%$ .
Angle $= \frac{\text{percentage}}{100\%} \times 360^\circ$ : $1\%$ is $3.6^\circ$ , $10\%$ is $36^\circ$ , $25\%$ is $90^\circ$ .
Amount in a sector $= \frac{\text{angle}}{360^\circ} \times$ total; a difference of amounts comes from the difference of the angles.
If $a^\circ$ stands for $q$ , the total is $\frac{360}{a} \times q$ ; if $p\%$ stands for $q$ , the total is $\frac{100}{p} \times q$ .
A missing angle is $360^\circ$ minus the others; angles in terms of $x$ add up to $360^\circ$ , which gives an equation for $x$ .
Two pie charts with different totals: equal angles mean equal fractions, not equal numbers. Work out each number from its own total.

Before you start

What a Pie Chart Shows

The angle of a sector

Example 1: Reading a pie chart

Fractions and Percentages from Angles, and Back

Fraction, percentage and angle

Example 2: Fractions and percentages from angles

Example 3: From a percentage to an angle

Finding an Amount from an Angle

An amount from an angle

Example 4: The number of students in a sector

Finding the Whole from One Sector

The whole from one sector

Example 5: The whole from one sector

Example 6: The whole from a percentage

Finding a Missing Angle

A missing angle

Example 7: A missing angle

Example 8: Angles in terms of xxx

Comparing Two Pie Charts

Equal angles need not mean equal numbers

Example 9: Two schools

Common mistakes

Practice

Practice 1: Siti's day

Practice 2: Percentages and angles

Practice 3: Saturday afternoons

Practice 4: Favourite subjects

Practice 5: A family's spending

Practice 6: Ali's pocket money

Practice 7: Sports Day

Practice 8: A level outing

Practice 9: The whole from a difference

Practice 10: Angles in a ratio

Practice 11: Drinks at the canteen

Practice 12: Two pie charts of pocket money

Key Points

Example 8: Angles in terms of $x$