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We know that the sum of the interior ang...

We know that the sum of the interior angles of a triangle is`180^0` . Show that the sums of eth interior angles of polygons with `3,4,5,6,` sides for an arithmetic progression. Find the sum of the interior angles of or a 21 sided polygon.

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To solve the problem step by step, we will first derive the formula for the sum of the interior angles of a polygon and then show that the sums for polygons with 3, 4, 5, and 6 sides form an arithmetic progression. Finally, we will calculate the sum of the interior angles of a 21-sided polygon. ### Step 1: Formula for the Sum of Interior Angles The sum of the interior angles \( S \) of an \( n \)-sided polygon can be calculated using the formula: \[ S = 180(n - 2) \] where \( n \) is the number of sides of the polygon. ...
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