FIND THE MISSING SIDES OF THE POLYGON IF EXTERIOR ANGLE GIVEN

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.