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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 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.    \(\angle SQU\)

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

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

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

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

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

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

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

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

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 024

 

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

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

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

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

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