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| Theorem 1 |
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| In a polygon of 'n' sides, the sum of the interior angles is equal to (2n - 4) right angles. |
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| ABCDE is an n sided polygon. |
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| The sum of the interior angles = (2n - 4) right angles |
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| Take any point O inside the polygon. Join OA, OB, OC. |
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Sum of 'n' interior angles = (2n - 4)  90o. |
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 Each interior angle of a regular polygon |
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| [Since in a regular polygon, all the interior angles are equal]. |
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| If the sides of a convex polygon are produced in order (clockwise or anticlockwise), the sum of the exterior angles is 4 right angles. |
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 = 4 right angles = 4  90o |
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 Each exterior angle for a regular polygon of n sides  |
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| Number of sides of a regular polygon |
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| 2. At each vertex, one interior angle + one exterior angle = 180o. |
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| How many sides has a regular polygon with each interior angle equal to 144o? |
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| [Each interior angle + each exterior angle = 180o] |
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| 144o + each exterior angle = 180o |
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 each exterior angle = 180o - 144o |
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| = 36o. |
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 Number of sides  |
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| = 10 |
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The sum of the interior  of a regular polygon is 1080o. How many sides are there? |
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| The sum of the interior angles |
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| = (2n - 4) x 90o |
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| = 1080o |
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| (2n - 4) x 90 = 1080 |
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2n - 4 = |
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| 2n = 16 |
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 n = 8 |
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 The polygon has 8 sides. |
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