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Solving Problems, SM-Bank 027

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

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\(45°\)

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\(\text{Angle above}\ \angle (3x)^{\circ} = (180-3x)^{\circ}\ \ \text{(180° in a straight line)}\)

\(180-3x\) \(=x\ \ \text{(corresponding angles)} \)  
\(4x\) \(=180\)  
\(x^{\circ}\) \(=\dfrac{180}{4}\)  
  \(=45^{\circ}\)  

Solving Problems, SM-Bank 026

Find the value of \(x^{\circ}\) in the diagram, giving reasons for your answer.   (3 marks)
 

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\(15°\)

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\(\text{Extend the parallel line on the left:}\)
 

\(\text{Angle opposite}\ \angle ABC = 3x^{\circ}\ \ \text{(vertically opposite)}\)

\(\angle DEB = 360-(90+135) = 135^{\circ}\ \ \text{(360° about a point)} \)

\(3x+135\) \(=180\ \ \text{(cointerior angles)} \)  
\(3x\) \(=180-135\)  
\(x^{\circ}\) \(=\dfrac{45}{3}\)  
  \(=15^{\circ}\)  

Solving Problems, SM-Bank 025

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

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\(11°\)

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\(\angle ADE + \angle DAC = 180^{\circ}\ \ \text{(cointerior angles)}\)

\(\angle ADE = 180-92=88^{\circ}\)

\(44+4x\) \(=88\)  
\(4x\) \(=44\)  
\(x^{\circ}\) \(=\dfrac{44}{4} \)  
  \(=11^{\circ}\)  

Solving Problems, SM-Bank 023

Find the value of \(x^{\circ}\) in the diagram, giving reasons for your answer.   (3 marks)
 

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\(50°\)

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\(\text{Extend the middle parallel line:}\)
 

\(\text{Alternate angles are equal}\ (x^{\circ}) \).

\(\text{Cointerior angles sum to 180° (110° and 70°)}\)

\(x^{\circ} = 120-70=50^{\circ} \)

Area, SM-Bank 157

An Aussie Rules football team has booked half of the SCG for a training session. The field available to them under this booking covers 8257 square metres.

Assuming the SCG is perfectly round, determine its diameter, giving your answer in metres to 1 decimal place.  (2 marks)

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\(145.0\ \text{m}\)

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\(\text{Area of full SCG}\ =2 \times 8257 = 16\ 514 \ \text{m}^{2}\)

\(A\) \(=\pi r^{2} \)
\(16\ 514\) \(= \pi r^2\)
\(r^{2}\) \(=\dfrac{16\ 514}{\pi} \)
\(r\) \(=\sqrt{5256.569…}\)
  \(=72.5022…\ \text{m} \)

 
\(\therefore\ \text{Diameter}\ = 2 \times 72.502 = 145.0\ \text{m (1 d.p.)} \)

Area, SM-Bank 156

The semi-circle, pictured below, has an area of 32 square centimetres.
 

Calculate the diameter of the semi-circle, giving your answer to 2 decimal places.  (2 marks)

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\(9.03\ \text{cm}\)

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\(\text{Area of full circle}\ =2 \times 32 = 64 \ \text{cm}^{2}\)

\(A\) \(=\pi r^{2} \)
\(64\) \(= \pi r^2\)
\(r^{2}\) \(=\dfrac{64}{\pi} \)
\(r\) \(=\sqrt{20.3718…}\)
  \(=4.5135…\ \text{cm} \)

 
\(\therefore\ \text{Diameter}\ = 2 \times 4.513 = 9.03\ \text{cm (2 d.p.)} \)

Area, SM-Bank 155

A semi-circle has an area of 470 square centimetres.

Calculate the diameter of the semi-circle, giving your answer to 1 decimal place.  (2 marks)

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\(34.6\ \text{cm}\)

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\(\text{Area of full circle}\ =2 \times 470 = 940\ \text{cm}^{2}\)

\(A\) \(=\pi r^{2} \)
\(940\) \(= \pi r^2\)
\(r^{2}\) \(= \dfrac{940}{\pi} \)
\(r\) \(=\sqrt{299.211…}\)
  \(=17.30\ \text{cm}\)

 
\(\therefore\ \text{Diameter}\ = 2 \times 17.30 = 34.6\ \text{cm (1 d.p.)}\)

Area, SM-Bank 150

The cross-section of the circular road tunnel, pictured below, has an area of \(46.24\pi \) square metres.
 

Calculate the radius of the tunnel.  (2 marks)

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\(6.8\ \text{m}\)

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\(A\) \(=\pi r^{2} \)
\(46.24 \pi\) \(= \pi r^2\)
\(r^{2}\) \(=46.24\)
\(r\) \(=\sqrt{46.24}\)
  \(=6.8\ \text{m}\)

Area, SM-Bank 154

The entrance to a tunnel, pictured below, is a semi-circle with an area of \(28.88\pi \) square metres.
 

Calculate the diameter of the tunnel.  (2 marks)

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\(7.6\ \text{m}\)

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\(\text{Area of full circle}\ =2 \times 28.88\pi = 57.76\pi \ \text{m}^{2}\)

\(A\) \(=\pi r^{2} \)
\(57.76 \pi\) \(= \pi r^2\)
\(r^{2}\) \(=57.76\)
\(r\) \(=\sqrt{57.76}\)
  \(=7.6\ \text{m}\)

Area, SM-Bank 151

The circle pictured below has an area of \(144\pi \) square centimetres.
 

Calculate the radius of the circle.  (2 marks)

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\(12\ \text{cm}\)

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\(A\) \(=\pi r^{2} \)
\(144 \pi\) \(= \pi r^2\)
\(r^{2}\) \(=144\)
\(r\) \(=\sqrt{144}\)
  \(=12\ \text{cm}\)

Area, SM-Bank 153

A circular cricket ground has an area of 11 028 square metres.

Determine the radius of the cricket ground, in metres, giving your answer to 1 decimal place.   (2 marks)

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\(59.2\ \text{m}\)

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\(A\) \(=\pi r^{2} \)
\(11\ 028\) \(= \pi r^2\)
\(r^{2}\) \(=\dfrac{11\ 028}{\pi}\)
\(r\) \(=\sqrt{3510.321…}\)
  \(=59.247…\)
  \(=59.2\ \text{m (1 d.p.)}\)

Area, SM-Bank 152

If a circle has an area of 100 square millimetres, find the radius of the circle, giving your answer to 2 decimal places.  (2 marks)

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\(5.64\ \text{mm}\)

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\(A\) \(=\pi r^{2} \)
\(100\) \(= \pi r^2\)
\(r^{2}\) \(=\dfrac{100}{\pi}\)
\(r\) \(=\sqrt{31.8309}\)
  \(=5.641…\)
  \(=5.64\ \text{mm (2 d.p.)}\)

Solving Problems, SM-Bank 001

Two boats leave from Fremantle. One sails to the Wharf at Rottnest Island and the other sails to Cervantes.

The direction each boat sailed is shown in the map below.
 

Determine the value of `x°` on the map.   (2 marks)

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`50°`

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`text(Alternate angles are equal)`

`60` `= x + 10` 
`:.x` `= 50^@` 

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`

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`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`

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`/_ 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`

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

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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`

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`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.

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

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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.

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

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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.

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

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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.    \(\angle SQU\)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Area, SM-Bank 149

A rhombus has an area of 250 square centimetres. If one diagonal measures 10 centimetres, find the length of the other diagonal.  (2 marks)

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\(50\ \text{cm}\)

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\(\text{Area of rhombus}=250\ \text{cm}^2\)

\(\text{Length of diagonal:}\ x=10\ \text{m}\)

\(A\) \(=\dfrac{1}{2}xy\)
\(250\) \(=\dfrac{1}{2}\times 10\times y\)
\(5y\) \(=250\)
\(y\) \(=\dfrac{250}{5}\)
  \(=50\ \text{cm}\)

 
\(\therefore\ \text{The other diagonal is }50\ \text{cm long.}\)

Area, SM-Bank 148

A rhombus has an area of 140.8 square metres. If one diagonal measures 16 metres, find the length of the other diagonal.  (2 marks)

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\(17.6\ \text{m}\)

Show Worked Solution

\(\text{Area of rhombus}=140.8\ \text{m}^2\)

\(\text{Length of diagonal:}\ x=16\ \text{m}\)

\(A\) \(=\dfrac{1}{2}xy\)
\(140.8\) \(=\dfrac{1}{2}\times 16\times y\)
\(8y\) \(=140.8\)
\(y\) \(=\dfrac{140.8}{8}\)
  \(=17.6\ \text{m}\)

 
\(\therefore\ \text{The other diagonal is }17.6\ \text{m long.}\)

Area, SM-Bank 147

Calculate the area of the following rhombus in millimetres squared.  (2 marks)

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\(96\ \text{mm}^2\)

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\(\text{Length of diagonal 1:}\ x=16\ \text{mm}\)

\(\text{Length of diagonal 2:}\ y=12\ \text{mm}\)

\(\text{Area of rhombus}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 16\times 12\)
  \(=96\ \text{mm}^2\)

Area, SM-Bank 146

Calculate the area of the following rhombus. All measurements are in metres.   (2 marks)

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\(90.24\ \text{m}^2\)

Show Worked Solution

\(\text{Length of diagonal 1:}\ x=14.1\ \text{m}\)

\(\text{Length of diagonal 2:}\ y=12.8\ \text{m}\)

\(\text{Area of rhombus}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 14.1\times 12.8\)
  \(=90.24\ \text{m}^2\)

Area, SM-Bank 145

Calculate the area of the following rhombus. All measurements are in metres.   (2 marks)

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\(76.44\ \text{m}^2\)

Show Worked Solution

\(\text{Length of diagonal 1:}\ x=2\times 4.2=8.4\ \text{m}\)

\(\text{Length of diagonal 2:}\ y=2\times 9.1=18.2\ \text{m}\)

\(\text{Area of rhombus}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 8.4\times 18.2\)
  \(=76.44\ \text{m}^2\)

Area, SM-Bank 144

Calculate the area of the following rhombus. All measurements are in centimetres.   (2 marks)

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\(484\ \text{cm}^2\)

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\(\text{Length of diagonal 1:}\ x=2\times 11=22\ \text{cm}\)

\(\text{Length of diagonal 2:}\ y=2\times 22=44\ \text{cm}\)

\(\text{Area of rhombus}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 22\times 44\)
  \(=484\ \text{cm}^2\)

Area, SM-Bank 143

Calculate the area of the following rhombus. All measurements are in millimetres.   (2 marks)

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\(24\ \text{mm}^2\)

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\(\text{Length of diagonal 1:}\ x=2\times 3=6\ \text{mm}\)

\(\text{Length of diagonal 2:}\ y=2\times 4=8\ \text{mm}\)

\(\text{Area of rhombus}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 6\times 8\)
  \(=24\ \text{mm}^2\)

Area, SM-Bank 142

Calculate the area of the following kite. All measurements are in millimetres.   (2 marks)

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\(180\ \text{mm}^2\)

Show Worked Solution

\(\text{Length of diagonal 1:}\ x=4+11=15\ \text{mm}\)

\(\text{Length of diagonal 2:}\ y=2\times 12=24\ \text{mm}\)

\(\text{Area of kite}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 34\times 20\)
  \(=180\ \text{mm}^2\)

Area, SM-Bank 141

Calculate the area of the following kite. All measurements are in metres.   (2 marks)

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\(340\ \text{m}^2\)

Show Worked Solution

\(\text{Length of diagonal 1:}\ x=26+8=34\ \text{m}\)

\(\text{Length of diagonal 2:}\ y=2\times 10=20\ \text{m}\)

\(\text{Area of kite}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 34\times 20\)
  \(=340\ \text{m}^2\)

Area, SM-Bank 140

Calculate the area of the following kite. All measurements are in centimetres.   (2 marks)

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\(156\ \text{cm}^2\)

Show Worked Solution

\(\text{Length of diagonal 1:}\ x=8+18=26\ \text{cm}\)

\(\text{Length of diagonal 2:}\ y=2\times 6=12\ \text{cm}\)

\(\text{Area of kite}\) \(=\dfrac{1}{2}xy\)
  \(=\dfrac{1}{2}\times 26\times 12\)
  \(=156\ \text{cm}^2\)

Area, SM-Bank 139

The diagram shows a sector with an angle of 120° cut from a circle with radius 10 m.

What is the area of the sector? Write your answer correct to 1 decimal place.  (2 marks)

NOTE:  \(\text{Sector area}=\dfrac{\theta}{360}\times \pi r^2\)

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\(104.7\ \text{m}^2\ (1\text{ d.p.})\)

Show Worked Solution
\(\text{Sector area}\) \(=\dfrac{\theta}{360}\times \pi r^2\)
  \(=\dfrac{120}{360}\times \pi\times 10^2\)
  \(=104.719\dots\)
  \(\approx 104.7\ \text{m}^2\ (1\text{ d.p.})\)