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Special Properties, SMB-025

A quadrilateral is pictured below.
 

What is the value of `x`?   (3 marks)

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`126^@`

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`text{Sum of exterior angles = 360°}`

`y^{\circ}` `=360-(127+114+65)`  
  `=360-306`  
  `=54^{\circ}`  

 
`:.x^{\circ}=180-54 = 126^{\circ}\ \ \text{(180° in straight line)}`

Special Properties, SMB-026

A pentagon is pictured below, where one internal angle is a right angle.
 

What is the value of `x`?   (3 marks)

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`130^@`

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`y^{\circ}=180-100 = 80^{\circ}\ \ \text{(180° in straight line)}`

`text{Sum of exterior angles = 360°}`

`z^{\circ}` `=360-(70+70+90+80)`  
  `=360-310`  
  `=50^{\circ}`  

 
`:.x^{\circ}=180-50 = 130^{\circ}\ \ \text{(180° in straight line)}`

Special Properties, SMB-024

A quadrilateral is drawn below.
 

What is the value of `x`?   (3 marks)

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`117^@`

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`y^{\circ}=180-75 = 105^{\circ}\ \ \text{(180° in straight line)}`

`text{Sum of exterior angles = 360°}`

`z^{\circ}` `=360-(130+105+62)`  
  `=360-297`  
  `=63^{\circ}`  

 
`:.x^{\circ}=180-63 = 117^{\circ}\ \ \text{(180° in straight line)}`

Special Properties, SMB-030

A regular decagon is pictured below.
 

  1. What is the value of `x`?   (2 marks)

  2. What is the size of an internal angle of a decagon?   (2 marks)

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i.    `36^@`

ii.   `144^@`

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i.    `text{Sum of exterior angles = 360°}`

`text{Since the decagon is regular, all external angles are equal.}`

`:.x^{\circ}= 360/10 = 36^{\circ}`

  
ii.    `text{Method 1: Using exterior angle}`

`text{Internal angle}` `=180-\text{exterior angle}`
  `=180-36`
  `=144^{\circ}`

  
`text{Method 2: Using Internal angle sum formula}`

`text{Sum of internal angles}` `=(n-2) xx 180`
  `=(10-2) xx 180`
  `=1440^{\circ}`

  
`:.\ text{Internal angle}\ = 1440/10 = 144^{\circ}`

Special Properties, SMB-024

A quadrilateral is drawn below.

What is the value of `x`?   (3 marks)

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`117^@`

Show Worked Solution

`y^{\circ}=180-75 = 105^{\circ}\ \ \text{(180° in straight line)}`

`text{Sum of exterior angles = 360°}`

`z^{\circ}` `=360-(130+105+62)`  
  `=360-297`  
  `=63^{\circ}`  

 
`:.x^{\circ}=180-63 = 117^{\circ}\ \ \text{(180° in straight line)}`

Special Properties, SMB-023

A pentagon is drawn below.
 

What is the value of `x`?   (3 marks)

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`99^@`

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`z^{\circ}=180-110 = 70^{\circ}\ \ \text{(180° in straight line)}`

`text{Sum of exterior angles = 360°}`

`y^{\circ}` `=360-(72+82+70+55)`  
  `=360-279`  
  `=81^{\circ}`  

 
`:.x^{\circ}=180-81 = 99^{\circ}\ \ \text{(180° in straight line)}`