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Angle Basics, SM-Bank 004 MC

Brianna plotted the points  `A-F`  on a grid paper, as shown below.

She then joined some of the points together with lines.

Which of these pairs of lines are parallel?

  1. `AF and AC`
  2. `AD and CF`
  3. `AE and BD`
  4. `AD and BD`
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`C`

Show Worked Solution

`AE and BD\ text(are parallel.)`

\(\Rightarrow C\)

Angle Basics, SM-Bank 003 MC

Lines `AB` and `CD` are parallel.

Line `EF` intersects lines `AB` and `CD` as shown.
 

 naplan-2016-20mc

Which pair of angles are equal?

  1. `/_ FQA and /_ FQB`
  2. `/_ CPQ and /_ AQE`
  3. `/_ CPQ and /_ PQB`
  4. `/_ DPE and /_ FPD`
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`C`

Show Worked Solution

`/_ CPQ and /_ PQB\ \ \ text{(alternate angles)}`

`=>C`

Angle Basics, SM-Bank 002 MC

Lines `AB` and `CD` are parallel.

Line `EF` intersects lines `AB` and `CD` as shown.
 

Which pair of angles are equal?

  1. `/_ EPB and /_ EPA`
  2. `/_ CQE and /_ APF`
  3. `/_ FQD and /_ FQC`
  4. `/_ CQE and /_ FPB`
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`D`

Show Worked Solution

`/_ CQE = /_ FPB\ \ text{(alternate angles)}`

`=>D`

Angle Basics, SM-Bank 001

The diagram below shows a transversal intersecting two parallel lines.

On the diagram, label the following:
 

  1. One pair of corresponding angles using the label "×" to identify the angles   (1 mark)

  2. One pair of cointerior angles using a dot \((\cdot)\) to identify the angles   (1 mark)

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\(\text{One solution (of many possibilities):}\)
 

Show Worked Solution

i. & ii.

\(\text{One solution (of many possibilities):}\)
 

Angle Basics, SM-Bank 1 MC

Craig is a town planner and needs to know the angles that streets make with each other.
 

He knows that Tombs Street and Horan Street are parallel.

What is the size of the shaded angle on the map?

  1. `60^@`
  2. `45^@`
  3. `30^@`
  4. `120^@`
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`A`

Show Worked Solution

`text(Corresponding angles are equal.)`

`:.\ text(Shaded angle) = 60°`

`=>A`

Angle Basics, SM-Bank 002

The diagram below shows a transversal intersecting two parallel lines.
 

On the diagram, identify

  1. One pair of alternate angles using a tick \((\checkmark)\) to identify the angles.   (1 mark)

  2. One pair of vertically opposite angles using a dot \((\cdot)\) to identify the angles.   (1 mark)

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i. & ii.

\(\text{One solution (of many possibilities):}\)
 

Show Worked Solution

i. & ii.

\(\text{One solution (of many possibilities):}\)
 

Angle Basics, SM-Bank 003

The diagram below shows a transversal intersecting two parallel lines.
 

On the diagram, label the following:

  1. One pair of cointerior angles using a tick \((\checkmark)\) to identify the angles.   (1 mark)

  2. One pair of alternate angles using a dot \((\cdot)\) to identify the angles.   (1 mark)

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i. & ii.

\(\text{One solution (of many possibilities):}\)
 

Show Worked Solution

i. & ii.

\(\text{One solution (of many possibilities):}\)
 

Angle Basics, SM-Bank 004

The diagram below shows a transversal intersecting two parallel lines.
 

On the diagram, identify

  1. One pair of vertically opposite angles using the label "×" to identify the angles.   (1 mark)

  2. One pair of corresponding angles using a dot \((\cdot)\) to identify the angles.   (1 mark)

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i. & ii.

\(\text{One solution (of many possibilities):}\)
 

Show Worked Solution

i. & ii.

\(\text{One solution (of many possibilities):}\)
 

Angle Basics, SM-Bank 005

The diagram below shows two parallel lines intersected by transversal \(RV\).
 

  1. Name the angle that is vertically opposite \(\angle TUR\).   (1 mark)

  2. Name the angle that is corresponding to \(\angle PQV\).   (1 mark)

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i.     \(\angle WUV\)

ii.    \(\angle WUV\)

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i.     \(\angle WUV\)
 

 

ii.    \(\angle WUV\)
 

Angle Basics, SM-Bank 006

The diagram below shows two parallel lines intersected by transversal \(RV\).
 

  1. Name the angle that is alternate to \(\angle RUW\).   (1 mark)

  2. Name the angle that is vertically opposite to \(\angle WUV\).   (1 mark)
  3. Name the angle that is cointerior to \(\angle QUT\).   (1 mark)

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i.     \(\angle SQU\)

ii.    \(\angle TUR\)

iii.    \(\angle SQU\)

Show Worked Solution

i.     \(\angle SQU\ \text{or}\ \angle SQV\)
  

 

ii.    \(\angle TUR\)
 

iii.    \(\angle SQU\)
 

Angle Basics, SM-Bank 008

The diagram below shows two parallel lines intersected by transversal \(CG\).
 

  1. Name the angle that is vertically opposite to \(\angle CBA\).   (1 mark)

  2. Name the angle that is cointerior to \(\angle GBD\).   (1 mark)
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i.    \(\angle DBF\)

ii.    \(\angle EFB\)

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i.   \(\angle DBF\)

 

 
ii.  \(\angle EFB\)

Angle Basics, SM-Bank 009

Determine, giving reasons, if the two lines cut by the transversal in the diagram below are parallel.   (2 marks)
 

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\(\text{Vertically opposite angles are equal (see diagram).}\)

\(\text{Cointerior angles sum to 180°, and} \)

\(88+88 \neq 180^{\circ}\)

\(\therefore\ \text{Lines are not parallel.}\)

Show Worked Solution

\(\text{Vertically opposite angles are equal (see diagram).}\)

\(\text{Cointerior angles sum to 180°, and} \)

\(88+88 \neq 180^{\circ}\)

\(\therefore\ \text{Lines are not parallel.}\)

Angle Basics, SM-Bank 010

Determine, giving reasons, if the two lines cut by the transversal in the diagram below are parallel.   (1 mark)

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\(\text{Cointerior angles sum to 180°, and} \)

\(113 + 57 = 170^{\circ} \neq 180^{\circ}\)

\(\therefore\ \text{Lines are not parallel.}\)

Show Worked Solution

\(\text{Cointerior angles sum to 180°, and} \)

\(113 + 57 = 170^{\circ} \neq 180^{\circ}\)

\(\therefore\ \text{Lines are not parallel.}\)

Angle Basics, SM-Bank 011

The diagram below shows two parallel lines cut by a transversal.
 

Find the value of \(x^{\circ}\), giving reasons.   (1 mark)

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\(x=72^{\circ}\ \ \text{(corresponding angles)}\)

Show Worked Solution

\(x=72^{\circ}\ \ \text{(corresponding angles)}\)

Angle Basics, SM-Bank 012

The diagram below shows two parallel lines cut by a transversal.
 

Find the value of \(a^{\circ}\) and \(b^{\circ}\), giving reasons.   (2 marks)

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\(\text{One strategy:}\)

\(\text{Vertically opposite angles are equal (117°)}\).

\(a^{\circ} = 180-117=63^{\circ}\ \ \text{(cointerior angles)}\)

\(b^{\circ}=180-63=117^{\circ}\ \ \text{(180° in straight line)}\)

Show Worked Solution

\(\text{One strategy:}\)

\(\text{Vertically opposite angles are equal (117°)}\).

\(a^{\circ} = 180-117=63^{\circ}\ \ \text{(cointerior angles)}\)

\(b^{\circ}=180-63=117^{\circ}\ \ \text{(180° in straight line)}\)

Angle Basics, SM-Bank 14

A trapezium is pictured below.
 

Find the value of \(x^{\circ}\), giving reasons.   (2 marks)

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\(\text{A trapezium has one pair of parallel sides.}\)

\(x^{\circ} = 180-115 = 65^{\circ}\ \ \text{(cointerior angles)}\)

Show Worked Solution

\(\text{A trapezium has one pair of parallel sides.}\)

\(x^{\circ} = 180-115 = 65^{\circ}\ \ \text{(cointerior angles)}\)

Angle Basics, SM-Bank 024

 

Find the value of \(x^{\circ}\), giving reasons.   (2 marks)

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\(\text{Vertically opposite angles}\ = 87^{\circ} \).

\(x^{\circ} = 180-87=93^{\circ}\ \ \text{(cointerior angles)}\)

Show Worked Solution

\(\text{Vertically opposite angles}\ = 87^{\circ} \).

\(x^{\circ} = 180-87=93^{\circ}\ \ \text{(cointerior angles)}\)

Angle Basics, SM-Bank 023

 

Calculate the value of \(x^{\circ}\), giving reasons for your answer.   (2 marks)

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\(\text{Sum of angles about a point = 360}^{\circ} \)

\(x^{\circ} =132^{\circ}\ \)

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\(\text{Sum of angles about a point = 360}^{\circ} \)

\(x^{\circ}\) \(=360-(75+110+43) \)  
  \(=132^{\circ}\)  

Basic Angles, SM-Bank 022

 

Calculate the value of \(x^{\circ}\), giving reasons for your answer.   (2 marks)

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\(\text{Sum of angles about a point = 360}^{\circ} \)

\(x^{\circ} =75^{\circ}\ \)

Show Worked Solution

\(\text{Sum of angles about a point = 360}^{\circ} \)

\(x^{\circ}\) \(=360-(70+90+125) \)  
  \(=75^{\circ}\)  

Angle Basics, SM-Bank 021

The diagram below shows a right angle.
 

Calculate, giving reasons, the value of \(x^{\circ}\).   (1 mark)

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\(\text{Right angles = 90}^{\circ} \)

\(a^{\circ} =50^{\circ}\ \ \text{(complementary angles)}\)

Show Worked Solution

\(\text{Right angles = 90}^{\circ} \)

\(a+2+a-12\) \(=90\ \text{(complementary angles)}\)  
\(2a-10\) \(=90\)  
\(a^{\circ}\) \(=\dfrac{100}{2}\)  
  \(=50^{\circ}\)  

Angle Basics, SM-Bank 020

A straight line, as shown below, is split into two angles.
 

Calculate the value of both angles.   (3 marks)

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\(\text{Straight lines have 180}^{\circ}\ \text{about a point.}\)

\(p^{\circ}=45^{\circ}, (3p)^{\circ} = 3 \times 45 = 135^{\circ}\)

Show Worked Solution

\(\text{Straight lines have 180}^{\circ}\ \text{about a point.}\)

\(3p+p\) \(=180\ \ \text{(supplementary angles)}\)  
\(p^{\circ}\) \(=\dfrac{180}{4}\)  
  \(=45^{\circ}\)  

 
\(\therefore\ \text{Two angles:}\ p^{\circ}=45^{\circ}, (3p)^{\circ} = 3 \times 45 = 135^{\circ}\)

Angle Basics, SM-Bank 019

A straight line, as shown below, is split into two angles.
 

Calculate the value of \(x^{\circ}\), giving reasons.   (2 marks)

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\(\text{Straight lines have 180}^{\circ}\ \text{about a point.}\)

\(x^{\circ}=89^{\circ}\)

Show Worked Solution

\(\text{Straight lines have 180}^{\circ}\ \text{about a point.}\)

\(x+16+x-14\) \(=180\ \ \text{(supplementary angles)}\)  
\(2x+2\) \(=180\)  
\(x^{\circ}\) \(=\dfrac{178}{2}\)  
  \(=89^{\circ}\)  

Angle Basics, SM-Bank 018

A straight line, as shown below, is split into three angles.
 

Calculate the value of \(a^{\circ}\), giving reasons.   (2 marks)

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\(\text{Straight lines have 180}^{\circ}\ \text{about a point.}\)

\(a^{\circ} = 30^{\circ}\)

Show Worked Solution

\(\text{Straight lines have 180}^{\circ}\ \text{about a point.}\)

\(a+3a+2a\) \(=180\ \ \text{(supplementary angles)}\)  
\(a^{\circ}\) \(=\dfrac{180}{6}\)  
  \(=30^{\circ}\)  

Angle Basics, SM-Bank-017

The diagram below shows a right angle.
 

Calculate, giving reasons, the value of \(x^{\circ}\).   (1 mark)

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\(\text{Right angles = 90}^{\circ} \)

\(x^{\circ} = 90-40=50^{\circ}\ \ \text{(complementary angles)}\)

Show Worked Solution

\(\text{Right angles = 90}^{\circ} \)

\(x^{\circ} = 90-40=50^{\circ}\ \ \text{(complementary angles)}\)

Angle Basics, SM-Bank 016

 

Calculate, giving reasons, the value of \(x^{\circ}\).   (1 mark)

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\(\text{Straight line has adjacent right angles.}\)

\(x^{\circ} = 90-57=33^{\circ}\ \ \text{(complementary angles)}\)

Show Worked Solution

\(\text{Straight line has adjacent right angles.}\)

\(x^{\circ} = 90-57=33^{\circ}\ \ \text{(complementary angles)}\)

Angle Basics, SM-Bank 15

The diagram below has one pair of parallel lines.
 

Calculate, giving reasons, the value of \(x^{\circ}\).   (2 marks)

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\(\text{Alternate angles are equal (see diagram).}\)

\(\text{Angles in a straight line sum to 180°:} \)

\(x^{\circ} = 180-30=150^{\circ}\)

Show Worked Solution

\(\text{Alternate angles are equal (see diagram).}\)

\(\text{Angles in a straight line sum to 180°:} \)

\(x^{\circ} = 180-30=150^{\circ}\)

Angle Properties, SM-Bank 007

The diagram below shows two parallel lines intersected by transversal \(CG\).
 

  1. Name two angles that are complementary to \(\angle DBF\).   (2 marks)

  2. Name the angle that is corresponding to \(\angle HFG\).   (1 mark)

  3. Name the angle that is alternate to \(\angle CFH\).   (1 mark)
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i.     \(\text{Correct answers include two of:}\)

\(\angle DBC,\ \angle EFB,\ \angle GFH,\ \text{or}\ \angle GBA.\)

ii.    \(\angle ABF\)

iii.  \(\angle DBF\)

Show Worked Solution

i.     \(\text{Complementary angles sum to 180°.}\)

\(\text{Correct answers include two of:}\)

\(\angle DBC,\ \angle EFB,\ \angle GFH,\ \text{or}\ \angle GBA.\)
 

ii.    \(\angle ABF\)

 

 
iii.  \(\angle DBF\)