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Fill in the blanks.i. Each interior angles of a regular octagon is (......)°.ii. The sum of all interior angle of a regular hexagon is (......)°.iii. Each exterior angle of a regular polygon is 60°. This polygon is a ...... . iv. Each interior angle of a regular polygon is 108°. This polygon is a ...... . v. A pentagon has ...... diagonals. |
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Answer» i. 135° Exterior Angle = \(\frac{360}{8}\) [n represents no of sides of polygon] = 45° Interior Angle + Exterior Angle = 180o Interior Angle = 180 – 45 = 135° ii. 720° Sum of Interior Angle = (n - 2)× 180° = (6 - 2) × 180 ° = 720° iii. Hexagon Exterior Angle = \(\frac{360}{n}\) 60 = \(\frac{360}{n}\) N = \(\frac{360}{60}\) = 6 No. of Sides is 6. So, it is a hexagon. iv. Pentagon Interior Angle = 108° Exterior Angle = 180° - 108° = 72° No. of Sides = \(\frac{360}{72}\) = 5 So, it is a pentagon. v. 5 No. of diagonals = \(\frac{n(n\,-\,3)}{2}\) [n is No. of Sides] = \(\frac{5\times(5\,-\,3)}{2}\) = 5 |
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