Find the sum of the measures of the intieior angles of each polygon.
-hexagon
-pentagon
-quadrilateral
-octagon
-16-gon
-27-gon
please
https://www.mathsisfun.com/geometry/interior-angles-polygons.html
8x+10+6x+2=180
To find the sum of the measures of the interior angles of each polygon, you can use the formula:
Sum of interior angles = (n - 2) * 180 degrees,
where 'n' represents the number of sides of the polygon.
Now let's apply this formula to each polygon:
1. Hexagon:
A hexagon has 6 sides, so the sum of its interior angles is:
(6 - 2) * 180 = 4 * 180 = 720 degrees.
2. Pentagon:
A pentagon has 5 sides, so the sum of its interior angles is:
(5 - 2) * 180 = 3 * 180 = 540 degrees.
3. Quadrilateral:
A quadrilateral has 4 sides, so the sum of its interior angles is:
(4 - 2) * 180 = 2 * 180 = 360 degrees.
4. Octagon:
An octagon has 8 sides, so the sum of its interior angles is:
(8 - 2) * 180 = 6 * 180 = 1080 degrees.
5. 16-gon:
A 16-gon has 16 sides, so the sum of its interior angles is:
(16 - 2) * 180 = 14 * 180 = 2520 degrees.
6. 27-gon:
A 27-gon has 27 sides, so the sum of its interior angles is:
(27 - 2) * 180 = 25 * 180 = 4500 degrees.
So, the sum of the measures of the interior angles for each polygon is:
Hexagon: 720 degrees
Pentagon: 540 degrees
Quadrilateral: 360 degrees
Octagon: 1080 degrees
16-gon: 2520 degrees
27-gon: 4500 degrees.