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If each interior angle of a regular polygon is 135°, then find the number of diagonals of the polygon.
  • a)
    12
  • b)
    14
  • c)
    16
  • d)
    20
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If each interior angle of a regular polygon is 135°, then find the...
Each interior angle of a regular polygon is 135,
⇒ Exterior angle = 180° - Interior angle = 45°
⇒ Number of sides of polygon = 360°/Exterior angle = 8
∴ Number of diagonals = n(n - 3)/2 = 8 × (8 - 3)/2 = 20, where n is the number of sides of a polygon.
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If each interior angle of a regular polygon is 135°, then find the...
Each interior angle of a regular polygon is 135,
⇒ Exterior angle = 180° - Interior angle = 45°
⇒ Number of sides of polygon = 360°/Exterior angle = 8
∴ Number of diagonals = n(n - 3)/2 = 8 × (8 - 3)/2 = 20, where n is the number of sides of a polygon.
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If each interior angle of a regular polygon is 135°, then find the number of diagonals of the polygon.a)12b)14c)16d)20Correct answer is option 'D'. Can you explain this answer?
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