Geometry, NAPX-E4-NC30 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

721

Question

Thorfinn was designing a viking shield using 9 identical isosceles triangles, as shown in the diagram below.

How many degrees is the angle marked x\large x?

Worked Solution

Angles at centre of circle
= 3609\dfrac{360}{9}
= 40°\degree

Since triangles are isosceles,
180 = 40 + 2x\large x
2x\large x = 140
x\large x = 70°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Thorfinn was designing a viking shield using 9 identical isosceles triangles, as shown in the diagram below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-E4-NC30-SA.svg 280 indent vpad How many degrees is the angle marked $\large x$?
workedSolution
sm_nogap Angles at centre of circle
>>|| |-| |= $\dfrac{360}{9}$| |= 40$\degree$|

sm_nogap Since triangles are isosceles,
||| |-:|-| |180|= 40 + 2$\large x$| |2$\large x$|= 140| |$\large x$|= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
70
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
correctAnswer070

°\degree

Variant 1

DifficultyLevel

720

Question

Terra was designing a new frisbee using 3 identical isosceles triangles, as shown in the diagram below.

How many degrees is the angle marked x\large x?

Worked Solution

Angles at centre of circle
= 3603\dfrac{360}{3}
= 120°\degree

Since triangles are isosceles,
180 = 120 + 2x\large x
2x\large x = 60
x\large x = 30°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Terra was designing a new frisbee using 3 identical isosceles triangles, as shown in the diagram below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-E4-NC30-SA_v4.svg 150 indent2 vpad How many degrees is the angle marked $\large x$?
workedSolution
sm_nogap Angles at centre of circle
>>|| |-| |= $\dfrac{360}{3}$| |= 120$\degree$|

sm_nogap Since triangles are isosceles,
||| |-:|-| |180|= 120 + 2$\large x$| |2$\large x$|= 60| |$\large x$|= {{{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

723

Question

Glory was designing a new logo for her catering business using 5 identical isosceles triangles, as shown in the diagram below.

How many degrees is the angle marked p\large p?

Worked Solution

Angles at centre of circle
= 3605\dfrac{360}{5}
= 72°\degree

Since triangles are isosceles,
180 = 72 + 2p\large p
2p\large p = 108
p\large p = 54°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Glory was designing a new logo for her catering business using 5 identical isosceles triangles, as shown in the diagram below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-E4-NC30-SA_v3.svg 160 indent vpad How many degrees is the angle marked $\large p$?
workedSolution
sm_nogap Angles at centre of circle
>>|| |-| |= $\dfrac{360}{5}$| |= 72$\degree$|

sm_nogap Since triangles are isosceles,
||| |-:|-| |180|= 72 + 2$\large p$| |2$\large p$|= 108| |$\large p$|= {{{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 3

DifficultyLevel

725

Question

Bergan was designing a chicken coup using 8 identical isosceles triangles, as shown in the diagram below.

How many degrees is the angle marked m\large m?

Worked Solution

Angles at centre of circle
= 3608\dfrac{360}{8}
= 45°\degree

Since triangles are isosceles,
180 = 45 + 2m\large m
2m\large m = 135
m\large m = 67.5°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Bergan was designing a chicken coup using 8 identical isosceles triangles, as shown in the diagram below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-E4-NC30-SA_v2.svg 220 indent vpad How many degrees is the angle marked $\large m$?
workedSolution
sm_nogap Angles at centre of circle
>>|| |-| |= $\dfrac{360}{8}$| |= 45$\degree$|

sm_nogap Since triangles are isosceles,
||| |-:|-| |180|= 45 + 2$\large m$| |2$\large m$|= 135| |$\large m$|= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
67.5
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
correctAnswer067.5

°\degree

Variant 4

DifficultyLevel

727

Question

Bilbo was designing a new thatched roof for his cottage using 6 identical isosceles triangles, as shown in the diagram below.

How many degrees is the angle marked y\large y?

Worked Solution

Angles at centre of circle
= 3606\dfrac{360}{6}
= 60°\degree

Since triangles are isosceles,
180 = 60 + 2y\large y
2y\large y = 120
y\large y = 60°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Bilbo was designing a new thatched roof for his cottage using 6 identical isosceles triangles, as shown in the diagram below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-E4-NC30-SA_v1.svg 180 indent vpad How many degrees is the angle marked $\large y$?
workedSolution
sm_nogap Angles at centre of circle
>>|| |-| |= $\dfrac{360}{6}$| |= 60$\degree$|

sm_nogap Since triangles are isosceles,
||| |-:|-| |180|= 60 + 2$\large y$| |2$\large y$|= 120| |$\large y$|= {{{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 5

DifficultyLevel

728

Question

Walt was designing a ferris wheel for his theme park using 12 identical isosceles triangles, as shown in the diagram below.

How many degrees is the angle marked w\large w?

Worked Solution

Angles at centre of circle
= 36012\dfrac{360}{12}
= 30°\degree

Since triangles are isosceles,
180 = 30 + 2w\large w
2w\large w = 150
w\large w = 75°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Walt was designing a ferris wheel for his theme park using 12 identical isosceles triangles, as shown in the diagram below. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-E4-NC30-SA_v5.svg 260 indent vpad How many degrees is the angle marked $\large w$?
workedSolution
sm_nogap Angles at centre of circle
>>|| |-| |= $\dfrac{360}{12}$| |= 30$\degree$|

sm_nogap Since triangles are isosceles,
||| |-:|-| |180|= 30 + 2$\large w$| |2$\large w$|= 150| |$\large w$|= {{{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

Tags