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You can have one angle that is 178 degrees and the remaining two that sum to 2 degrees. A very thin triangle.

If, on the other hand, you claim that the sum of all three angles is 178 degrees then there are two possible reasons. The more likely one is that you have made a mistake. Alternatively, the triangle is on a slightly concave surface.

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Q: How do you get 178 degrees out of a triangle?
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