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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)

Show Answers Only

i.    `36^@`

ii.   `144^@`

Show Worked Solution

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}`