Angles and Polygons

Question

Find the measure of each interior angle and each exterior angle of a regular 18-gon.

The measure of each interior angle is ____, and the measure of each exterior angle is ____.

Answer 1

The formula for finding the measure of interior angles on a regular polygon is ((n-2) * 180) / n where n is the number of sides of the polygon. In this case, we have an 18-gon, so our n value is 18.

If we plug this in, we get:

First, plug in: ((18-2) * 180) / 18

Simplify: (16*180)/18

Simplify: 2880/18

Solve: 160

So our interior angles must have a measure of 160 degrees. The exterior and interior angles must add up to be equal to 180, so we simply have to subtract our interior angle measure from 180. This gives us an exterior angle measure of 180-160 = 20. So our exterior angles have a measure of 20 degrees.

Answer 2

for a triangle interior angles are 60 degrees, (3-2)(180)/3= 60. exterior 120 180-60=120

for a square interior = 90, exterior 90. (4-2)(180)/4= 90 180-90 = 90

for pentagon interior = (5-2)(180)/5 = 3(36)=108 exterior=180-108 = 72

hexagon (6-2)(180)/6 = 4(30) = 120, exterior =60 (flip side to triangle)

heptagon (7-2)(180)/7 =5(180)/7=900/7= 128 4/7. exterior=51 3/7

octagon (8-2)180/8 = 6(45)/2=135. exterior= 45

decagon (9-2)180/9 = 7(20) =140 exterior=40

11 sided polygon (11-2)180/11= 9(180)/11 = 1620/11=147 3/11. exterior=32 8/11

12 sided (12-2)180/12 = 10(15)=150. exterior 30

13 sided (13-2)180/13=11(180)/13=1910/13. exterior=180-1910/13

14 sided (14-2)180/14 = 12(90/7 =1080/7=154 2/7 exterior=25 5/7

15 sided (15-2)180/15=13(12)=156 exterior=24

16-gon (16-2)180/16 = 7(45)/2=315/2=157.5 ext. 22.5

17-gon (17-2)180/17 =

18-gon (18-2)180/180=16(10)= 160, ext=20

...

180-gon (180-2)180/180 = 178. ext=2

n sided polygon = (n-2)180/n ext=180-interior

as n approaches infinity, interior approaches 180, ext approaches 0

infinity sided polygon approaches a circle

Answer 3

Sum of interior angles = (n-2) 180 where n is number of sides. Each interior angle of a regular polygon would be (n-2) 180 / n. Here n = 18.

Sum of exterior angles is 360, so each exterior angle of a regular polygon would be 360/n.