Geometry, NAPX-I3-CA26 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

633

Question

Rob creates a design that is made up of 3 rectangles and 2 straight lines, as shown below.



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

Worked Solution


Base angles of isosceles triangle = 30°\degree

Since 180°\degree in a straight line:
a\large a°\degree = 180−(90+30)180 - (90 + 30)
= 60°\degree
∴x\therefore \large x = 180−60180 - 60
= 120°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Rob creates a design that is made up of 3 rectangles and 2 straight lines, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-I3-CA26-SA.svg 280 indent3 vpad
What is the size of angle $\large x \degree$?
workedSolution
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/06/NAPX-I3-CA26-SA-Answer.svg 280 indent3 vpad
Base angles of isosceles triangle = 30$\degree$ Since 180$\degree$ in a straight line:
||| |-|-| |$\large a$$\degree$|= $180 - (90 + 30)$| ||= 60$\degree$|
||| |-|-| |$\therefore \large x$|= $180 - 60$| ||= {{{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 1

DifficultyLevel

634

Question

Chloe creates a design that is made up of 3 rectangles and 2 straight lines, as shown below.



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

Worked Solution


Base angles of isosceles triangle = 55°\degree

Since 180°\degree in a straight line:
a\large a°\degree = 180−(90+55)180 - (90 + 55)
= 35°\degree
∴x\therefore \large x = 180−35180 - 35
= 145°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Chloe creates a design that is made up of 3 rectangles and 2 straight lines, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I3-CA26-SA_v1.svg 240 indent3 vpad
What is the size of angle $\large x \degree$?
workedSolution
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I3-CA26-SA_v1_ws.svg 260 indent3 vpad
Base angles of isosceles triangle = 55$\degree$ Since 180$\degree$ in a straight line:
||| |-|-| |$\large a$$\degree$|= $180 - (90 + 55)$| ||= 35$\degree$|
||| |-|-| |$\therefore \large x$|= $180 - 35$| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
145
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
correctAnswer0145

°\degree

Variant 2

DifficultyLevel

632

Question

Dudley creates a design that is made up of 3 rectangles and 2 straight lines, as shown below.



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

Worked Solution


Base angles of isosceles triangle = 45°\degree

Since 180°\degree in a straight line:
a\large a°\degree = 180−(90+45)180 - (90 + 45)
= 45°\degree
∴x\therefore \large x°\degree = 180−45180 - 45
= 135°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Dudley creates a design that is made up of 3 rectangles and 2 straight lines, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I3-CA26-SA_v2a.svg 220 indent3 vpad
What is the size of angle $\large x \degree$?
workedSolution
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I3-CA26-SA_v2a_ws.svg 220 indent3 vpad
Base angles of isosceles triangle = 45$\degree$ Since 180$\degree$ in a straight line:
||| |-|-| |$\large a$$\degree$|= $180 - (90 + 45)$| ||= 45$\degree$|
||| |-|-| |$\therefore \large x$$\degree$|= $180 - 45$| ||= {{{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

635

Question

Lidija creates a design that is made up of 3 rectangles and 2 straight lines, as shown below.



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

Worked Solution


Base angles of isosceles triangle = 51°\degree

Since 180°\degree in a straight line:
a\large a°\degree = 180−(90+51)180 - (90 + 51)
= 39°\degree
∴x\therefore \large x°\degree = 180−39180 - 39
= 141°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Lidija creates a design that is made up of 3 rectangles and 2 straight lines, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I3-CA26-SA_v3.svg 260 indent3 vpad
What is the size of angle $\large x \degree$?
workedSolution
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I3-CA26-SA_v3_ws.svg 260 indent3 vpad
Base angles of isosceles triangle = 51$\degree$ Since 180$\degree$ in a straight line:
||| |-|-| |$\large a$$\degree$|= $180 - (90 + 51)$| ||= 39$\degree$|
||| |-|-| |$\therefore \large x$$\degree$|= $180 - 39$| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
141
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
correctAnswer0141

°\degree

Variant 4

DifficultyLevel

636

Question

Bernie creates a design that is made up of 3 rectangles and 2 straight lines, as shown below.



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

Worked Solution


Base angles of isosceles triangle = 27°\degree

Since 180°\degree in a straight line:
a\large a°\degree = 180−(90+27)180 - (90 + 27)
= 63°\degree
∴x\therefore \large x°\degree = 180−63180 - 63
= 117°\degree

Question Type

Answer Box

Variables

Variable nameVariable value
question
Bernie creates a design that is made up of 3 rectangles and 2 straight lines, as shown below.
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I3-CA26-SA_v4.svg 310 indent3 vpad
What is the size of angle $\large x \degree$?
workedSolution
sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/10/Geom_NAPX-I3-CA26-SA_v4_ws.svg 310 indent3 vpad
Base angles of isosceles triangle = 27$\degree$ Since 180$\degree$ in a straight line:
||| |-|-| |$\large a$$\degree$|= $180 - (90 + 27)$| ||= 63$\degree$|
||| |-|-| |$\therefore \large x$$\degree$|= $180 - 63$| ||= {{{correctAnswer0}}}{{{suffix0}}}|
correctAnswer0
117
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
correctAnswer0117

°\degree

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