Regular polygon has all sides equal in length and all angles equal in size.
The sum of interior angles of n sided polygon is
s = (n - 2) x 180°
Sum of exterior angles of any polygon is 360 degree.
Problem 1 :
Find the number of sides of a regular polygon whose each exterior angle measures 60°.
Solution :
Sum of all exterior angles = 360°
n × 60 = 360
n = 360/60
n = 6
Hence, the number of sides in the polygon is 6.
Problem 2 :
An exterior angle and the interior angle of a regular polygon are in the ratio 2:7. Find the number of sides of the polygon.
Solution :
Let x be the interior angle, then 180-x be the exterior angle.
(180-x) : x = 2 : 7
(180-x)/x = 2 / 7
2x = 7(180-x)
2x = 1260 - 7x
2x + 7x = 1260
9x = 1260
x = 1260/9
x = 40
Exterior angle is 40 degree. Interior angle = 140
Hence, the number of sides in the polygon is 9.
Problem 3 :
Each exterior angle of a regular polygon is 20⁰. Work out the number of sides of the polygon.
Solution :
Exterior angle of the regular polygon = 20
Each interior angle = 180 - 20
= 160
Measure of each interior angle = [(n - 2) 180]/n
160 = (180/n)(n - 2)
160n/180 = n - 2
8n/9 = n - 2
8n = 9(n - 2)
8n = 9n - 18
8n - 9n = -18
-n = -18
n = 18
So, the number of sides of the polygon is 18.
Problem 4 :
The number of sides of a regular polygon whose each exterior angle is 60° is
Solution :
Exterior angle of the regular polygon = 60
Each interior angle = 180 - 60
= 120
Measure of each interior angle = [(n - 2) 180]/n
120 = (180/n)(n - 2)
120n/180 = n - 2
2n/3 = n - 2
2n = 3(n - 2)
2n = 3n - 6
2n - 3n = -6
-n = -6
n = 6
So, the number of sides of the polygon is 6.
Problem 5 :
The interior angle of a regular polygon is four times its exterior angle. How many sides does the polygon have ?
Solution :
Let x be the interior angle, then 180 - x be the exterior angle.
x = 4(180 - x)
x = 720 - 4x
Adding 4x, we get
x + 4x = 720
5x = 720
x = 720/5
x = 144
Interior angle = 144.
Measure of each interior angle = [(n - 2) 180]/n
144 = (180/n)(n - 2)
1440n/180 = n - 2
4n/5 = n - 2
4n = 5(n - 2)
4n = 5n - 10
4n - 5n = -10
-n = -10
n = 10
So, the number of sides of the polygon is 10.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM