Question

Each exterior angle of a regular polygon is approximately 51.43. How many sides does the polygon have?

Answer 1

i think it is S= (n-2)180

Answer 2

remember you are looking for the number of sides.

Answer 3

for "N" sided polygon, there are "N" number of exterior angles.
sum of all exterior angles should be 360

Answer 4

to find 1 angle of a regular convex polygon of n sides = 360/n

Answer 5

so, the general formula for exterior angle for "N" sides would be,
\[\theta={360^\circ\over N}\]

Answer 6

\[51.43=\frac{ 360 }{ n}\]

Answer 7

yes!

Answer 8

now do the rest

Answer 9

this is true for a "Regular convex polygon" only

Answer 10

n should equal the amount of sides a polygon has right???

Answer 11

yep. and that is what you are finding here..

Answer 12

how many sides did you find out?

Answer 13

im strying to figure it out

Answer 14

\[51.43={360\over n}\\
n\times51.43=\cancel{n}\times{360\over \cancel{n}}
\]

Answer 15

similarly, divide both sides by "51.43"

Answer 16

so i divide 360 by 51.43???

Answer 17

yes

Answer 18

ok i got 6.99 is that correct ???

Answer 19

now, can you have 6.99 number of sides?
NO
so, round it to the nearest integer.
that means, you have "7" sides to the polygon

Answer 20

ohh ok i was going to do that thank you :D

Answer 21

good. yw