Problem

In a 19 -sided polygon, what is the sum of a) the interior angles? b) the exterior angles?

Solution

Step 1 :Let n be the number of sides in the polygon. In this case, n = 19.

Step 2 :To find the sum of the interior angles of a polygon, we can use the formula \((n-2) \times 180\).

Step 3 :Substitute n with 19: \((19-2) \times 180\).

Step 4 :Simplify the expression: \(17 \times 180\).

Step 5 :Calculate the sum: \(3060\).

Step 6 :\(\boxed{\text{a) The sum of the interior angles of a 19-sided polygon is 3060 degrees.}}\)

Step 7 :The sum of the exterior angles of any polygon is always 360 degrees.

Step 8 :\(\boxed{\text{b) The sum of the exterior angles of a 19-sided polygon is 360 degrees.}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/30649/

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