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

1 Answer

Answer:

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

Explanation:

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^@#