Question

can u help me
What is the sum of the measures of the interior angles of a polygon with twelve sides?

Answer 1

if a polygon has 12 sides, how many "central" angles would it have?

Answer 2

i dont kmow

Answer 3

or rather, 12 sides would equate a pie cut into 12 pieces, since the outer edges count as the sides right?

Answer 4

teh central angles are where all the pieces meet in the middle

Answer 5

does that make sense?

Answer 6

hold on

Answer 7

wat teh

Answer 8

wat is teh

Answer 9

take an octagon (8 sides) for example

Answer 10

"teh" is a typo of the word "the" :)

Answer 11

i dont get it

Answer 12

.... what part dont you get?

Answer 13

central angles

Answer 14

do you see the picture I drew of an octagon?

Answer 15

ya

Answer 16

do you see how all the lines converge to the center of it?

Answer 17

ya

Answer 18

we need to determine the size of an angle that is at the center in order to determine the value of an "interior" angle.

Answer 19

ok

Answer 20

your question poses 12 sides; and each side has i its own central angle.

we use this fact and the knowledge that a full circle is made up of 360 degrees.

Answer 21

so u divide by 12

Answer 22

thats correct; 360/12 should equal what ... 30?

Answer 23

that is only one step in the process ... its a useful step tho :)

Answer 24

thanks

Answer 25

the next step is to recognise that the shape is cut up into identical isocolese triangles .. im sure i typoed that

Answer 26

we know one angle of any of the triangles is going to be 30; and that all 3 angles of a triangle add up to equal 180 right?

Answer 27

here is a standard piece of our 12 sided polygon so far

Answer 28

if we can determine the value of a base angle we will know exactly 1/2 the value of an interior angle

Answer 29

or simply put; if we can determine the value of the other 2 angles, that will be the same value as an interior angle

Answer 30

180 - 30 = 150; which is the answer we want

Answer 31

360/ etc....:-) (BTW, Wolfram is wrong, exterir angle is used by nearly everyone except them)

Answer 32

ok

Answer 33

we can do these steps each time or generalize the concept

Answer 34

180 - (360/#sides) = interior angle; this is a good formula, but it can be simplified as needed

Answer 35

ok