What is the sum of the interior and the exterior angles of a 100-gon?
Would the interior be (100-2)180 = 98*180=17640 degrees.
is the exterior figured out 360/100= 3.6 degrees.
To find the sum of the interior angles of a polygon, you can use the formula (n-2) * 180 degrees, where n represents the number of sides of the polygon.
In this case, you have a 100-gon, so the sum of the interior angles would be (100 - 2) * 180 = 98 * 180 = 17,640 degrees.
Now, to find the measure of each interior angle, you divide the sum by the number of sides. So, each interior angle of a 100-gon would be 17,640 / 100 = 176.4 degrees.
To find the measure of each exterior angle, you use the fact that the sum of the interior and exterior angles of any polygon is always 180 degrees (a straight angle). Since you already know that the measure of each interior angle is 176.4 degrees, you can subtract that from 180 to find the measure of each exterior angle:
180 - 176.4 = 3.6 degrees.
Therefore, each exterior angle of a 100-gon would be 3.6 degrees.
Lastly, to find the sum of the interior and exterior angles together, you add each interior angle to each exterior angle:
176.4 + 3.6 = 180 degrees.
So, the sum of the interior and exterior angles of a 100-gon is 180 degrees.