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# Suppose the measures of the interior angles of a convex nonagon are nine numbers each separated by a value of 1 degree from its neighbors what is the measure of the third smallest angle?

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Answered Jul 20Maths

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Beatrix HuissoonUndergraduate at the University of Cambridge, with lots of tutoring experience28 students helped

In any shape, all internal angles must add up to 360°. If this was a regular nonagon (all internal angles are the same), each internal angle would be 360÷9=40°. We know that each internal angle is different from its neighbour by just 1°, so the internal angles must be 36°, 37°, 38°, 39°, 40°, 41°, 42°, 43° and 44°. (Check they all add up to 360°!) This means the answer to your question is 38°.