If the external angle of a polygon is 45° then find the number of diagonal in this polygon.

  1. 20
  2. 40
  3. 15
  4. 30

Answer (Detailed Solution Below)

Option 1 : 20
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Detailed Solution

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Given:

External angle = 45° 

Formula used:

External angle = (360°/n)

Number of diagonal of a n side polygon = (n2 - 3n)/2

Where, n = Equal to the number of side of a polygon

Calculation:

External angle = (360°/n)

⇒ 45° = (360°/n)

⇒ n = 8 

Now, Number of diagonal of a 'n' side polygon

⇒ (n2 - 3n)/2

⇒ (64 - 24)/2

⇒ 20

∴ The number of diagonal is 20.

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