What is the maximum number of angles less than $150^{\circ}$ that a non-crossing 2017-sided polygon can have, all of whose angles are strictly less than $180^{\circ}$?

## 3 High School Eliminators: Statements

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Answer: 11. If the angles are $180-x_{i}$, then we have $x_{i}>0$ and $x_{1}+\cdots+x_{2017}=360$, so at most 11 of the $x_{i}$ can be greater than 30. We can verify that conversely there exists such a polygon.

## 5 High School Eliminatory: Solutions