Geometry, NAPX-I4-CA25 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

708

Question

A regular pentagon can be divided into three triangles from one vertex, as shown below.



What is the size of the internal angle x\large x°\degree?

Worked Solution

Sum of interior angles
= 3 × 180
= 540°\degree

∴x\therefore \large x°\degree = 540 ÷ 5
= 108°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
A regular pentagon can be divided into three triangles from one vertex, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2020/09/NAPX-I4-CA25rev.svg 160 indent3 vpad
What is the size of the internal angle $\large x$$\degree$?
workedSolution
sm_nogap Sum of interior angles
>||| |-|-| ||= 3 × 180| ||= 540$\degree$|

||| |-|-| |$\therefore \large x$$\degree$|= 540 ÷ 5| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
108
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
correctAnswer0108

°\degree

Variant 1

DifficultyLevel

708

Question

A regular hexagon can be divided into four triangles from one vertex, as shown below.



What is the size of the internal angle x\large x°\degree?

Worked Solution

Sum of interior angles
= 4 × 180
= 720°\degree

∴x\therefore \large x°\degree = 720 ÷ 6
= 120°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
A regular hexagon can be divided into four triangles from one vertex, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I4-CA25-SA_v1.svg 160 indent3 vpad
What is the size of the internal angle $\large x$$\degree$?
workedSolution
sm_nogap Sum of interior angles
>||| |-|-| ||= 4 × 180| ||= 720$\degree$|

||| |-|-| |$\therefore \large x$$\degree$|= 720 ÷ 6| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
120
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
correctAnswer0120

°\degree

Variant 2

DifficultyLevel

711

Question

A regular octagon can be divided into six triangles from one vertex, as shown below.



What is the size of the internal angle x\large x°\degree?

Worked Solution

Sum of interior angles
= 6 × 180
= 1080°\degree

∴x\therefore \large x°\degree = 1080 ÷ 8
= 135°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
A regular octagon can be divided into six triangles from one vertex, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I4-CA25-SA_v2.svg 260 indent3 vpad
What is the size of the internal angle $\large x$$\degree$?
workedSolution
sm_nogap Sum of interior angles
>||| |-|-| ||= 6 × 180| ||= 1080$\degree$|

||| |-|-| |$\therefore \large x$$\degree$|= 1080 ÷ 8| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
135
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
correctAnswer0135

°\degree

Variant 3

DifficultyLevel

714

Question

A regular decagon can be divided into eight triangles from one vertex, as shown below.



What is the size of the internal angle x\large x°\degree?

Worked Solution

Sum of interior angles
= 8 × 180
= 1440°\degree

∴x\therefore \large x°\degree = 1440 ÷ 10
= 144°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
A regular decagon can be divided into eight triangles from one vertex, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I4-CA25-SA_v3.svg 260 indent3 vpad
What is the size of the internal angle $\large x$$\degree$?
workedSolution
sm_nogap Sum of interior angles
>||| |-|-| ||= 8 × 180| ||= 1440$\degree$|

||| |-|-| |$\therefore \large x$$\degree$|= 1440 ÷ 10| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
144
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
correctAnswer0144

°\degree

Variant 4

DifficultyLevel

711

Question

A regular nonagon can be divided into seven triangles from one vertex, as shown below.



What is the size of the internal angle x\large x°\degree?

Worked Solution

Sum of interior angles
= 7 × 180
= 1260°\degree

∴x\therefore \large x°\degree = 1260 ÷ 9
= 140°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
A regular nonagon can be divided into seven triangles from one vertex, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I4-CA25-SA_v4.svg 260 indent3 vpad
What is the size of the internal angle $\large x$$\degree$?
workedSolution
sm_nogap Sum of interior angles
>||| |-|-| ||= 7 × 180| ||= 1260$\degree$|

||| |-|-| |$\therefore \large x$$\degree$|= 1260 ÷ 9| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
140
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
correctAnswer0140

°\degree

Variant 5

DifficultyLevel

713

Question

A regular dodecagon can be divided into ten triangles from one vertex, as shown below.



What is the size of the internal angle x\large x°\degree?

Worked Solution

Sum of interior angles
= 10 × 180
= 1800°\degree

∴x\therefore \large x°\degree = 1800 ÷ 12
= 150°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
A regular dodecagon can be divided into ten triangles from one vertex, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I4-CA25-SA_v5.svg 280 indent3 vpad
What is the size of the internal angle $\large x$$\degree$?
workedSolution
sm_nogap Sum of interior angles
>||| |-|-| ||= 10 × 180| ||= 1800$\degree$|

||| |-|-| |$\therefore \large x$$\degree$|= 1800 ÷ 12| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
150
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
correctAnswer0150

°\degree

Tags

  • ms_ca