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Solving Problems, SM-Bank 029

What is the value of \(x^{\circ}\) in this diagram?   (2 marks)

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\(54^{\circ}\)

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\(\text{Adjacent angle to 144°}\ = 180-144=36^{\circ}\ \ \text{(180° in straight line)}\)

\(x^{\circ}= 180-(90 + 36)=54^{\circ}\ \ \text{(180° in straight line)}\)

Solving Problems, SM-Bank 022

In the diagram below, \(DG\) is parallel to \(BC\), and \(\angle ABC = 115^{\circ} \).
  

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

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\(\angle CBE = 180-115=65^{\circ}\ \ \text{(180° in a straight line)}\)

\(x^{\circ} = 65^{\circ}\ \ \text{(alternate angles)}\)

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\(\angle CBE = 180-115=65^{\circ}\ \ \text{(180° in a straight line)}\)

\(x^{\circ} = 65^{\circ}\ \ \text{(alternate angles)}\)

Solving Problems, SM-Bank 021

In the diagram below, \(BE\) is parallel to \(CD\), and \(\angle ABE = 160^{\circ} \).
  

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

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\(\angle DBE = 180-160=20^{\circ}\ \ \text{(180° in a straight line)}\)

\(180^{\circ}\) \(=x+20+110\ \ \text{(cointerior angles)} \)  
\(x^{\circ}\) \(=180-130\)  
  \(=50^{\circ}\)  
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\(\angle DBE = 180-160=20^{\circ}\ \ \text{(180° in a straight line)}\)

\(180^{\circ}\) \(=x+20+110\ \ \text{(cointerior angles)} \)  
\(x^{\circ}\) \(=180-130\)  
  \(=50^{\circ}\)  

Solving Problems, SM-Bank 020

In the diagram below, \(QR\) is parallel to \(SU\).
  

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

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\(\angle STP = 38^{\circ}\ \ \text{(corresponding angles)}\)

\((x+30)^{\circ}\) \(=180-38\ \ \text{(180° in straight line)} \)  
\(x^{\circ}\) \(=142-30\)  
  \(=112^{\circ}\)  
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\(\angle STP = 38^{\circ}\ \ \text{(corresponding angles)}\)

\((x+30)^{\circ}\) \(=180-38\ \ \text{(180° in straight line)} \)  
\(x^{\circ}\) \(=142-30\)  
  \(=112^{\circ}\)  

Solving Problems, SM-Bank 012

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

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\(\angle y^{\circ} = 180-(52+90) = 38^{\circ}\ \ \text{(180° in straight line)} \)

\(\angle x^{\circ}=38^{\circ}\ \ \text{(alternate angles)}\)

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\(\angle y^{\circ} = 180-(52+90) = 38^{\circ}\ \ \text{(180° in straight line)} \)

\(\angle x^{\circ}=38^{\circ}\ \ \text{(alternate angles)}\)

Solving Problems, SM-Bank 010

In the diagram below, \(BC\) is parallel to \(DE\) and \(\angle ACB\) is a right-angle.
 

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

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\(\text{Extend line}\ BC: \)
 

\(\angle GCF=180-120=60^{\circ}\ \ \text{(180° in a straight line)}\)

\(x^{\circ} = 60^{\circ} \ \ \text{(corresponding angles)}\)

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\(\text{Extend line}\ BC: \)
 

\(\angle GCF=180-120=60^{\circ}\ \ \text{(180° in a straight line)}\)

\(x^{\circ} = 60^{\circ} \ \ \text{(corresponding angles)}\)

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

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