What is the sum of the measures of the interior angles of a 25-sided polygon?

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Answer 1 · 2016-12-21T03:31:00

Sum of the measures of the interior angles of of a 25-sided polygon is $4140^@$

Sum of the measures of all the exterior angles of any polygon, irrespective of its number of sides is always $360^@$ .

As the measure of each pair of exterior and interior angles of a polygon adds up to $180^@$ ,

Sum of the measures of all the exterior angles and all interior angles of a 25-sided polygon is

$25xx180^@=4500^@$

Hence, sum of all the interior angles of of a 25-sided polygon is $(4500-360)^@=4140^@$

From the above information, we can see that for an $n$ sided polygon

Sum of interior angles = $(n-2)*180^@$