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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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\(\text{One strategy:}\)

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

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

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

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\(\text{One strategy:}\)

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

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

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

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 020

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

Calculate the value of both angles.   (3 marks)

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

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

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

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

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

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

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