Geometry, NAPX-F4-CA27 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

715

Question

Six identical triangles are used to make the figure below.

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

Worked Solution

Consider the centre angles of each triangle, c°\large c\degree
6 × c\times\ \large c°\degree = 180°\degree
c\large c°\degree = 30°\degree
∴x\therefore \large x°\degree = 180−(90+30)180 - (90 + 30)
= 60°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Six identical triangles are used to make the figure below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-F4-CA27-SA.svg 160 indent3 vpad What is the size of the angle marked $\large x \degree$?
workedSolution
Consider the centre angles of each triangle, $\large c\degree$ sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-F4-CA27-SA-Answer.svg 90 indent3 vpad
||| |-:|-| |6 $\times\ \large c$$\degree$|= 180$\degree$| |$\large c$$\degree$|= 30$\degree$| |$\therefore \large x$$\degree$|= $180 - (90 + 30)$| ||= {{{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 1

DifficultyLevel

717

Question

Three identical triangles are used to make the figure below.

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

Worked Solution

Consider the centre angles of each triangle, c°\large c\degree
3 × c\times\ \large c°\degree = 180°\degree
c\large c°\degree = 60°\degree
∴x\therefore \large x°\degree = 180−(90+60)180 - (90 + 60)
= 30°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Three identical triangles are used to make the figure below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-F4-CA27-SA_v1.svg 120 indent3 vpad What is the size of the angle marked $\large x \degree$?
workedSolution
Consider the centre angles of each triangle, $\large c\degree$ sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-F4-CA27-SA-Answer.svg 100 indent3 vpad
||| |-:|-| |3 $\times\ \large c$$\degree$|= 180$\degree$| |$\large c$$\degree$|= 60$\degree$| |$\therefore \large x$$\degree$|= $180 - (90 + 60)$| ||= {{{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 2

DifficultyLevel

719

Question

Four identical triangles are used to make the figure below.

What is the size of the angle marked y°\large y \degree?

Worked Solution

Consider the centre angles of each triangle, c°\large c\degree
4 × c\times\ \large c°\degree = 180°\degree
c\large c°\degree = 45°\degree
∴y\therefore \large y°\degree = 180−(90+45)180 - (90 + 45)
= 45°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Four identical triangles are used to make the figure below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-F4-CA27-SA_v2.svg 130 indent3 vpad What is the size of the angle marked $\large y \degree$?
workedSolution
Consider the centre angles of each triangle, $\large c\degree$ sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-F4-CA27-SA-Answer.svg 90 indent3 vpad
||| |-:|-| |4 $\times\ \large c$$\degree$|= 180$\degree$| |$\large c$$\degree$|= 45$\degree$| |$\therefore \large y$$\degree$|= $180 - (90 + 45)$| ||= {{{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

719

Question

Five identical triangles are used to make the figure below.

What is the size of the angle marked m°\large m \degree?

Worked Solution

Consider the centre angles of each triangle, c°\large c\degree
5 × c\times\ \large c°\degree = 180°\degree
c\large c°\degree = 36°\degree
∴m\therefore \large m°\degree = 180−(90+36)180 - (90 + 36)
= 54°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Five identical triangles are used to make the figure below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-F4-CA27-SA_v3.svg 140 indent3 vpad What is the size of the angle marked $\large m \degree$?
workedSolution
Consider the centre angles of each triangle, $\large c\degree$ sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-F4-CA27-SA-Answer.svg 90 indent3 vpad
||| |-:|-| |5 $\times\ \large c$$\degree$|= 180$\degree$| |$\large c$$\degree$|= 36$\degree$| |$\therefore \large m$$\degree$|= $180 - (90 + 36)$| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
54
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
correctAnswer054

°\degree

Variant 4

DifficultyLevel

721

Question

Twelve identical triangles are used to make the figure below.

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

Worked Solution

Consider the centre angles of each triangle, c°\large c\degree
12 × c\times\ \large c°\degree = 180°\degree
c\large c°\degree = 15°\degree
∴x\therefore \large x°\degree = 180−(90+15)180 - (90 + 15)
= 75°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Twelve identical triangles are used to make the figure below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-F4-CA27-SA_v4.svg 180 indent3 vpad What is the size of the angle marked $\large x \degree$?
workedSolution
Consider the centre angles of each triangle, $\large c\degree$ sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-F4-CA27-SA-Answer.svg 90 indent3 vpad
||| |-:|-| |12 $\times\ \large c$$\degree$|= 180$\degree$| |$\large c$$\degree$|= 15$\degree$| |$\therefore \large x$$\degree$|= $180 - (90 + 15)$| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
75
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
correctAnswer075

°\degree

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