Question

Given the regular polygon, what is the measure of each numbered angle?

Answer 1

http://gyazo.com/bef6396485344d6469a11f0e95df6041

Answer 2

I think a polygon has 108 per angle.

Answer 3

But given this, it should be smaller.

Answer 4

I think it has 30 in it, so perhaps the latter two answers.

Answer 5

what makes you believe its 30? i come to 120 and get stuck

Answer 6

the measure of the internal angle of a regular polygon = \((n-2)*\dfrac{180}{n}\) where n is the number of sides. here we have 6 sides, so \(4*\dfrac{180}{6}=120\)

however it looks like each angle is being bisected by those lines drawn through the center. What do you think the measure of angle 2 is now?

Answer 7

Wouldn't it be 60?

Answer 8

yeah, and then notice that there's a triangle being made with angle 2 and 1 as 2 interior angles.
find the bottom angle first

Answer 9

I understand how angle 2 is 60, the part I don't understand is how 120 becomes 30 degrees when you are calculating angle 1. How did you calculate that to get 30 for angle 1?

Answer 10

I didn't say that was 30, that says <1 as in the measurement of angle 1

Answer 11

this is what we're working with

Answer 12

we found that each internal angle = 120 deg

Answer 13

and so we're left with

Answer 14

since a triangle adds up to 180 degrees you take 60 + 60 and get 120. so 180 - 120 = 60. so <1 = 60, and <2 = 60

Answer 15

I think so. The only problem I have with saying yes to the above work is I can't definitively say that those lines bisect the angles, it's just an assumption

Answer 16

thank you :)

Answer 17

anytime :D