Facts:
The sum of exterior angles of a polygon is 360°
The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360°/ number of sides.
Interior Angle = 180° − Exterior Angle
In this case:
E = exterior angle
I = interior angle
n = number of sides
The exterior angle of a regular polygon is equal to one third of the interior angle means:
E = I / 3
Multiply both sides by 3
3 E = I
I = 3 E
Interior Angle = 180° − Exterior Angle means:
I = 180° − E
Since I = 3 E
3 E = 180° − E
Add E to both sides
4 E = 180°
Divide both sides by 4
E = 180° / 4
E = 45°
I = 180° − E
I = 180° − 45°
I = 135°
The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360°/ number of sides means:
E = 360°/ n
Since E = 45°
45° = 360°/ n
Multiply both sides by n
45° • n = 360°
Divide both sided by 45°
n = 360°/ 45°
n = 8
Check of results:
E = 360°/ n
E = 360°/ 8
E = 45°
I = 180° − E
I = 180° − 45°
I = 135°
E = 45° = 135° / 3
E = I / 3
The exterior angle of a regular polygon is equal to one third of the interior angle .calculate the number of sides of the polygon
2 answers
360/n = 1/3 * 180(n-2)/n
n = 8
n = 8