Geometry, NAPX-G3-CA29 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

721

Question

Five lines of symmetry are drawn on a regular decagon pictured below.

What is the size of the angle between each line of symmetry at the centre of the decagon?

Worked Solution

There are 10 angles at the centre of the decagon of the same size.
∴\therefore Size of angle = 360 ÷ 10
= 36°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Five lines of symmetry are drawn on a regular decagon pictured below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/08/NAPX-G3-CA29-SA.svg 200 indent vpad What is the size of the angle between each line of symmetry at the centre of the decagon?
workedSolution
sm_nogap There are 10 angles at the centre of the decagon of the same size.
||| |-|-| |$\therefore$ Size of angle|= 360 ÷ 10| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
36
prefix0
suffix0
$\degree$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer036

°\degree

Variant 1

DifficultyLevel

720

Question

Three lines of symmetry are drawn on a regular hexagon pictured below.

What is the size of the angle between each line of symmetry at the centre of the hexagon?

Worked Solution

There are 6 angles at the centre of the hexagon of the same size.
∴\therefore Size of angle = 360 ÷ 6
= 60°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Three lines of symmetry are drawn on a regular hexagon pictured below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-G3-CA29-SA_v1.svg 180 indent vpad What is the size of the angle between each line of symmetry at the centre of the hexagon?
workedSolution
sm_nogap There are 6 angles at the centre of the hexagon of the same size.
||| |-|-| |$\therefore$ Size of angle|= 360 ÷ 6| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
60
prefix0
suffix0
$\degree$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer060

°\degree

Variant 2

DifficultyLevel

723

Question

Four lines of symmetry are drawn on a regular octagon pictured below.

What is the size of the angle between each line of symmetry at the centre of the octagon?

Worked Solution

There are 8 angles at the centre of the octagon of the same size.
∴\therefore Size of angle = 360 ÷ 8
= 45°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Four lines of symmetry are drawn on a regular octagon pictured below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-G3-CA29-SA_v2.svg 180 indent vpad What is the size of the angle between each line of symmetry at the centre of the octagon?
workedSolution
sm_nogap There are 8 angles at the centre of the octagon of the same size.
||| |-|-| |$\therefore$ Size of angle|= 360 ÷ 8| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
45
prefix0
suffix0
$\degree$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer045

°\degree

Variant 3

DifficultyLevel

725

Question

Six lines of symmetry are drawn on a regular dodecagon pictured below.

What is the size of the angle between each line of symmetry at the centre of the dodecagon?

Worked Solution

There are 12 angles at the centre of the dodecagon of the same size.
∴\therefore Size of angle = 360 ÷ 12
= 30°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Six lines of symmetry are drawn on a regular dodecagon pictured below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/11/Geom_NAPX-G3-CA29-SA_v3b.svg 300 indent vpad What is the size of the angle between each line of symmetry at the centre of the dodecagon?
workedSolution
sm_nogap There are 12 angles at the centre of the dodecagon of the same size.
||| |-|-| |$\therefore$ Size of angle|= 360 ÷ 12| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
30
prefix0
suffix0
$\degree$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer030

°\degree

Variant 4

DifficultyLevel

727

Question

Five lines of symmetry are drawn on a regular pentagon pictured below.

What is the size of the angle between each line of symmetry at the centre of the pentagon?

Worked Solution

There are 10 angles at the centre of the pentagon of the same size.
∴\therefore Size of angle = 360 ÷ 10
= 36°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Five lines of symmetry are drawn on a regular pentagon pictured below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-G3-CA29-SA_v3.svg 200 indent vpad What is the size of the angle between each line of symmetry at the centre of the pentagon?
workedSolution
sm_nogap There are 10 angles at the centre of the pentagon of the same size.
||| |-|-| |$\therefore$ Size of angle|= 360 ÷ 10| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
36
prefix0
suffix0
$\degree$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer036

°\degree

Variant 5

DifficultyLevel

723

Question

Three lines of symmetry are drawn on a equilateral triangle pictured below.

What is the size of the angle between each line of symmetry at the centre of the equilateral triangle?

Worked Solution

There are 6 angles at the centre of the equilateral triangle of the same size.
∴\therefore Size of angle = 360 ÷ 6
= 60°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Three lines of symmetry are drawn on a equilateral triangle pictured below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-G3-CA29-SA_v4.svg 200 indent vpad What is the size of the angle between each line of symmetry at the centre of the equilateral triangle?
workedSolution
sm_nogap There are 6 angles at the centre of the equilateral triangle of the same size.
||| |-|-| |$\therefore$ Size of angle|= 360 ÷ 6| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
60
prefix0
suffix0
$\degree$

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer060

°\degree

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