The sum of exterior angles of polygon is 360 degrees and all the interior angles are supplementary to all their corresponding exterior angles.
The sum of all interior angles of 100-gon is 17640 degrees.
Given that:
- The regular polygon given is of 100 sides.
To find:
Sum of all of its interior angles.
Theorem for sum of exterior angles of regular polygon:
Sum of all exterior angles of a regular polygon is [tex]360^\circ[/tex]
Each exterior angle has corresponding interior angle and vice versa.
Interior angle = 180 - its corresponding exterior angle
Summing it for 100 angles in given 100 gon, we get:
Sum of all interior angles = [tex]100 \times 180 - 360[/tex] = [tex]17,640^\circ[/tex]
Thus, the sum of all interior angles of 100-gon is 17640 degrees.
Learn more about interior angles of a regular polygon here:
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