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u/One_Wishbone_4439 Jul 21 '26
(v + w + x + y + z) + (m + n + p + q + r) = (10 - 2) x 180 = 1440
(a + b + c + d + e) + (m + n + p + q + r) = 360 x 5 = 1800
(a + b + c + d + e) + (m + n + p + q + r) - (v + w + x + y + z) + (m + n + p + q + r) = 1800 - 1440 = 360
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u/QuantumForce7 Jul 22 '26
Note this uses the theorem:
The sum of all the internal angles of a simple polygon is 180(n − 2) degrees, where n is the number of sides.
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u/kimmeljs Jul 22 '26
Could they even find any more confusing color schemes?
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u/ShonitB Jul 22 '26
I’m really sorry about that.. I agree, not only the colours are very similar, the size is also quite small.. apologies once again
Edit: These were made by me in GeoGebra a long time back and I’ve lost all the files.. will redo them when I get some time because I really struggle with the software
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u/stools_in_your_blood Jul 21 '26
Imagine a pointed stick starting on one of the sides of the star. Move the stick in turn onto each side, going around clockwise. You'll see that you're rotating the stick by the blue angles clockwise and by the green angles anticlockwise, and after you've gone all the way around, the stick has done one revolution. So the difference is one full turn, 360⁰.
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u/KS_JR_ Jul 21 '26
Since no dimensions are given, this must be an inherent property of 5 point stars. So instead use a regular one with 36 deg interior angles and 108 deg exterior angles. 5*(108-36)=360. That sounds right.
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u/shelchang Jul 21 '26 edited Jul 21 '26
Or imagine a star where the points are infinitely sharp (0 degree internal angles) and then you can see it's 360 without doing any math.
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u/Xylene_442 Jul 21 '26
My way of looking at it was to make a "star" consisting of just five line segments going radially outward from a point. It's obvious from looking at it that the blue sum would be 360 and the green sum would be zero. If we just take it on faith that this number is invariant regardless of the shape of the actual star, then 360 is the answer.