I need some help with a mathematical question...determining an angle..many thanks!

[Chris Williams 2975]

I am working on a piece currently (a mirror with wood slats surrounding it)...without trying to make this too difficult (obviously I was asleep during geometry class as a kid!!) I am trying to determine the following:

Imagine a pizza/pie/cake...cut into 40 equal slices or pie shapes. The pizza is 40" in diameter resulting in a circumference of 125.6 inches. If it were cut into 40 equal pieces, what is the inside angle for each one (point of pizza/pie that all meet in middle)? For the life of me, I can't figure this out and I know it is something simple...so yes, I admit...I am ignorant today and many days before and after.

Am I calculating wrong when I assume that if there are 40 pieces, there would be 40 inside angles that would have to total up to 360 degrees = 9 degrees for each pointed angle?

Many many thanks for anyone who would be kind enough to help me. your time is greatly appreciated (and will ultimately make one happy wife when she gets her mirror done!)

Have a great night!

[Louis Brandt]

You are correct. 360 divided by 40 = 9 degrees. The diameter and circumference of the thing has no bearing on the angles. If you had the thing divided into 4 segments, each one would be 90 degrees (360 divided by 4 = 90).

[Mike Henderson]

Yep, there's 360 degrees in a circle. If you slice it into 40 equal slices, the inside angle will be 360/40, or 9 degrees.

Mike

[Chris Williams 2975]

Many thanks to all!! Stupid question, but I'm glad I was somewhere in the ballpark!

[Al Navas]

Chris,

You were on the money! But...

Were you also trying to calculate the length of the arc corresponding to each of the 40 pieces of the pie? If that is the case, the circumference is:

circumference = diameter * pi = 40 inches * 3.14 = 125.66 inches long

arc for each piece of the pie = 125.66 inches / 40 = 3.14 inches ;)


Al

[Pat Barry]

If the pieces you are cutting are going around the outside of a round mirror, forming the outside frame, and you want 40 pieces, then each part will need two angles of 4.5 degrees each. One of these cut at +4.5 degrees and the other at -4.5 degrees. 40 pieces, each with two angled cuts, totalling 360 degrees = 360 / 80 or 4.5 degrees. If you were only doing 20 pieces then each angle would be + and - 9 degrees.

[Forrest Bonner]

Chris, 360/40 does equal 9 but I would offer that if we could see a dwg of your mirror frame we might do a better job of answering your real concern. Your description of your frame is not very clear to me. The mirror has to be part of the 'pizza' doesn't it? The 40 pieces with a pointy end facing in around the mirror would look strange to me.
Forrest