how to calculate size of the exterior angle of a regular hexagon?

Question

how do you do it?

Answer 1

Hi. The hexagon has six equal angles. Each internal angle is 120 deg. Each external angle starts at 180 and has 60 deg added.

Answer 2

First, you can find the inner angle of the hexagon. To start, divide the hexagon into 6 equilateral triangles (by just drawing lines through the opposite vertexes). You would know that all of these angles are now 60 degrees. Since each angle in the hexagon is made up of 2 angles from equilateral triangles, the inner angles of the hexagon are 60*2=120 degrees. Then, around any given point, there's a total of 360 degrees. So the exterior angle is 360-120= 240 degrees.

Answer 3

by working them out? are you kidding me? maybe I should put my name on the paper too when you submit it.. anyway, I'll help you, but you'll get nowhere if I just work things out for you. 1. a hexagon has six sides, that means if you find the dot right in the middle of the hexagon and draw lines to the points, you have six triangles all with their top point touching and the bottom of each triangle is the side of the hexagon.. You know that a complete circle has 360 degrees.. so as the six triangles touch at the top, the angle of each one is one sixth of 360. so each is 60 degrees. Now, take each triangle. You know when you add up the angles in a triangle, they always add up to 180 degrees, and you also know that this is an isosceles triangle, the sides are the same and so the bottom two angles are the same too. So the top angle is 60 degrees, then you split the remaining 120 into the two angles and you get 60 each.. So this actually works out to be an equilateral triangle. If you did the drawing as I said, you'll see that the inside angle of a hexagon is made up of two corners of the triangles.. add those up. For the outside angle just draw a straight line touching one of the sides and it would be the angle between that line and the next side. For this, you should know that the angles at the straight line also add up to 180, so little math there too.. hint: you should get 60 degrees. Now.. before I work anything else out.. which I have no plan doing.. if you followed what I said, you can do the rest with no problems.. of course, if you don't and just get mad at me, you can wait for others on yahoo who'd be happy to help you, but you still won't know how to find this.. I wish you luck, contact me if you need more help..