💯 Maths

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?

1 answers
Answered Jul 20Maths
Beatrix's profile picture
Verified
Verified
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°.