Question

Examine the figure of the regular polygon below.
What is the value of x?

45

60

30

40

Answer 1

what do you think it is?

Answer 2

am not sure i just started polygons and i really dont get it

Answer 3

two ways to do this...

Answer 4

do you know what the sum of all the EXTERIOR angles of any polygon is?

Answer 5

always ...

Answer 6

is it the one that says n-2=180

Answer 7

no that's the other way:

the SUM of all INTERIOR angles of polygon is \(\large (n-2)\times 180\)

Answer 8

where n is the number of sides

Answer 9

oh well what is it for exterior then?

Answer 10

So in a REGULAR polygon: the measure of Each INTERIOR angle will be:
\[\Large{ (n-2)\cdot 180 \over n}\]

in a hexagon with 6 sides that gives us:
\[\Large {(4)\cdot 180 \over6}\]

Answer 11

so somehow i got 60 degrees...

Answer 12

that's 180/3 * 2 = 60*2 = 120 degrees