For the following regular polygons, find the following, round to the nearest tenth, if necessary.
1. 24-gon
2. 30-gon
3. Polygon with 40 sides
FOLLOWING WHAT?
I'm sorry I meant find
A) Sum of the interior angles
B) Measure of an interior angle
C) Measure of an exterior angle.
for those polygons
https://www.mathsisfun.com/geometry/polygons.html
To find the measures of interior angles and the sum of interior angles for regular polygons, we can use the formulas:
1. Interior angle measure of a regular polygon:
- The measure of each interior angle of a regular polygon with n sides can be found using the formula: (n-2) * 180 / n
- For a 24-gon, the measure of each interior angle is (24-2) * 180 / 24 = 1560 / 24 = 65 degrees (rounded to the nearest tenth).
2. Sum of interior angles of a regular polygon:
- The sum of the interior angles of any polygon can be found using the formula: (n-2) * 180 degrees.
- For a 30-gon, the sum of the interior angles is (30-2) * 180 = 28 * 180 = 5040 degrees (rounded to the nearest tenth).
3. For a polygon with 40 sides, we can apply the same formula:
- The measure of each interior angle is (40-2) * 180 / 40 = 1520 / 40 = 38 degrees (rounded to the nearest tenth).
So, the answers are:
1. The measure of each interior angle of a 24-gon is 65 degrees (rounded to the nearest tenth).
2. The sum of the interior angles of a 30-gon is 5040 degrees (rounded to the nearest tenth).
3. The measure of each interior angle of a 40-gon is 38 degrees (rounded to the nearest tenth).