Question

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

Answer 1

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^@`