The sun of the measures of the interior angles of various polygons are given. Set up an equation and solve to find the numbers of sides of each polygon.
6. 1080°
7. 1440°
8. 2340°
9. 180°
10. 3600°
11. 540°
6. Let n represent the number of sides of the polygon. The formula for the sum of the interior angles of a polygon is (n-2)*180°. So we can set up the equation:
(n-2)*180° = 1080°
n-2 = 1080°/180°
n-2 = 6
n = 6+2
n = 8
Therefore, the polygon has 8 sides.
7. Similarly, let n represent the number of sides of the polygon. The equation will be:
(n-2)*180° = 1440°
n-2 = 1440°/180°
n-2 = 8
n = 8+2
n = 10
Thus, the polygon has 10 sides.
8. Using the same method, for a polygon with n sides:
(n-2)*180° = 2340°
n-2 = 2340°/180°
n-2 = 13
n = 13+2
n = 15
Therefore, the polygon has 15 sides.
9. In this case, the sum of the interior angles is already given as 180°. Since a polygon can't have less than 3 sides, the equation would be:
(n-2)*180° = 180°
n-2 = 180°/180°
n-2 = 1
n = 1+2
n = 3
Hence, the polygon has 3 sides, which is a triangle.
10. For a polygon with n sides:
(n-2)*180° = 3600°
n-2 = 3600°/180°
n-2 = 20
n = 20+2
n = 22
The polygon has 22 sides.
11. Similarly, for a polygon with n sides:
(n-2)*180° = 540°
n-2 = 540°/180°
n-2 = 3
n = 3+2
n = 5
Therefore, the polygon has 5 sides, which is a pentagon.