Crazy Lightening
Imagine you are riding this super-crazy lightening strike from the cloud right on down. You take every turn with it, heading the way it does, and add up all the angles it makes on your right side. Make sure to include the one between the cloud base and the lightening, as well as the one at the end between the lightening and the ground. Assume that the cloud base and the ground are both perfectly horizontal and report your answer in degrees.
The answer is 3060.
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1 solution
An ordinary 18-sided polygon would have the sum of internal angles equal to ( 1 8 − 2 ) × 1 8 0 ∘ = 2 8 8 0 ∘ .
After taking off the two right angles added to close the figure, we would be left with 2 8 8 0 ∘ − 1 8 0 ∘ = 2 7 0 0 ∘ .
However, our polygon is taking additional turns. As you follow it, you turn to the right one full turn, which subtracts 3 6 0 ∘ , then you turn left two whole turns, adding 3 6 0 ∘ × 2 = 7 2 0 ∘ .
Altogether the correction adds up to positive 3 6 0 ∘ , giving you the answer of 2 7 0 0 ∘ + 3 6 0 ∘ = 3 0 6 0 ∘ .