Interior angle = 180 * (10-2) / 10 = 180 * 8 / 10 = 144
Exterior angle = 360 / number_of_sides = 360 / 10 = 36 degrees
Ratio (144:36 = 4:1)
Definitions:The exterior angle (e) is the angle created from the side and the imaginary line that would be if the adjacent side were to be extended beyond the vertices. The interior angle (i) plus the exterior angle (e) add up to 180 degrees, so i + e = 180.In a normal polygon, the sum of the exterior angle of all vertices adds up to 360 degrees; the sides do not overlap or cross. In a regular polygon each external angle is the same, and will divide evenly into 360 degrees to give the number of sides (n): 360 / e = n.
Proof:Given that the ratio of the two angles is 4 to 1: i = 4e.Now substitute: i + e = 180; 4e + e = 5e = 180.
e = 180 / 5 = 36 degrees.
i = 180 - e = 144 degrees.
360/e = 360/36 = 10 sides.
The interior angle of a regular normal polygon of n sides is: i = (n-2)*180/n.
For n=10: i = (10-2)*180/10 = 8*18 = 144 degrees, so it checks.
Other i to e ratios:1 to 2: 3 sides: triangle (trigon)2 to 2: 4 sides: tetrahedron (tetragon, square)
3 to 2: 5 sides: pentahedron (pentagon)
4 to 2: 6 sides: hexahedron (hexagon)
5 to 2: 7 sides: heptahedron
6 to 2: 8 sides: octahedron (octagon)
7 to 2: 9 sides: enneahedron (nonogon)
8 to 2: 10 sides: decahedron (decagon)
1440 degrees
1440 degrees
1800 degrees
360
If exterior angles are 120 then interior angles must be 60 so you have an equilateral triangle
Hint: in a regular polygon interior plus exterior = 180o, always.
360
1440 degrees
1440 degrees
1800 degrees
360
If exterior angles are 120 then interior angles must be 60 so you have an equilateral triangle
The interior angle of any regular polygon can be calculated using the formula 180 * (n - 2) / n, where n is the number of sides. In this case, since each exterior angle measures 72 degrees, the interior angle would be 180 - 72 = 108 degrees. So the measures of the interior angles in this regular polygon would be 108 degrees.
The sum of a regular polygon's interior angles is always equal to (n-2) * 180, where n is the number of sides in the polygon. Given that one exterior angle measures 40 degrees, we can find the interior angle by subtracting 40 from 180 degrees (since the exterior and interior angles are supplementary) to get 140 degrees. So, the sum of the interior angles of the regular polygon is 140 * n.
1440 degrees
540 degrees
Interior angle = 120 degrees Exterior angle = 60 degrees