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

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

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

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

Angle Basics, SM-Bank 15

The diagram below has one pair of parallel lines.
 

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

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

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

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

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

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

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

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.  \(\angle DBF\)