I don't understand how this equation calculates angle for hexagons

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In summary, the conversation discusses confusion around calculating the angle for hexagons using the equation 2pi/n, where n represents the number of sides. The person is trying to understand how this equation works and is questioning its accuracy based on their own calculations and a diagram from their book. They also mention that the angle being measured in radians may be causing their confusion.
  • #1
poetryrocksalo
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I don't understand how this equation calculates angle for hexagons...

Hi, I'm learning how to program and I've been studying graphics.

This quote from a programmer confuses me (the quote is a hyperlink to my source):

How does 2pi/n calculate the angle of two vertices relative to the center of a hexagon? I try to plug in some values to test it and the resulting angle is 1.047 degrees which is extremely small and I think I'm misunderstanding the answer.

I have a diagram in my book that also states that the above equation is the angle. I also tested my code (the angle is only a small part of it) and my drawHexagon app works. However, when I do the math, the angle from the center of the hexagon is always 1.047 degrees and that doesn't make sense to me.

Shouldn't the central angle be 60 degrees given that a hexagon has 6 sides?
 
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  • #2
The angles are being measured in radians.
2pi radians=360 degrees.
1.047 radians=60 degrees.
 
  • #3
lurflurf said:
The angles are being measured in radians.
2pi radians=360 degrees.
1.047 radians=60 degrees.

Thank you. I really need to brush up on my math.
 

1. How does the equation for calculating angles in hexagons work?

The equation for calculating angles in hexagons is based on the fact that the sum of all angles in a hexagon is equal to 720 degrees. This means that if we divide 720 by 6 (the number of sides in a hexagon), we get the measure of each angle, which is 120 degrees.

2. Why is the sum of angles in a hexagon equal to 720 degrees?

This can be explained by the fact that a hexagon can be divided into 6 triangles, and the sum of angles in each triangle is 180 degrees. Therefore, 6 x 180 = 1080 degrees. However, we need to subtract the 360 degrees that form the central angles of the hexagon, leaving us with 720 degrees for the sum of all angles.

3. Can this equation be used for all types of hexagons?

Yes, this equation can be used for all types of hexagons, whether they are regular or irregular. As long as the hexagon has 6 sides, the sum of angles will always be 720 degrees.

4. Is there a different equation for calculating angles in other types of polygons?

Yes, there are different equations for calculating angles in other types of polygons. For example, the sum of angles in a triangle is 180 degrees, in a quadrilateral it is 360 degrees, and in a pentagon it is 540 degrees. The equation for calculating angles in a polygon depends on the number of sides it has.

5. How can I use this equation to find the measure of a specific angle in a hexagon?

If you know the measure of all other angles in the hexagon, you can use the equation 720 - (sum of known angles) = measure of the unknown angle. For example, if you know that 4 angles in a hexagon are 60 degrees each, you can find the measure of the remaining angle by subtracting 240 (4 x 60) from 720, giving you 480 degrees for the unknown angle.

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