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If one of the internal angle of a regular polygon is 135°, Then find the number of diagonals in the polygon.1. 162. 183. 204. 24 |
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Answer» Correct Answer - Option 3 : 20 Given One of the internal angles of a regular polygon is 135° Concept Each interior angle of a regular polygon = [(n -2)/n] × 180° Number of diagonals = [n(n - 3)/2] Calculation ⇒ 135° = [(n -2)/n] × 180° ⇒ (135°/180°) = [(n -2)/n] ⇒ (3/4) = [(n -2)/n] ⇒ 3n = 4n - 8 ⇒ n = 8 Now, we get ⇒ Number of diagonals = 8(8 - 3)/2 ⇒ Number of diagonals = 20 ∴ Number of diagonals is 20 |
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