2. Kevin draws a point $P$ on a large sheet of paper. He then draws straight lines one by one that pass through the point $P$. How many lines must Kevin draw at least to be certain that there are two lines on the paper with an angle between them of less than 13 degrees?
A) 9
B) 13
C) 14
D) 27
E) 28

![](https://cdn.mathpix.com/cropped/2024_04_17_4e6ce4fdc7c7bcbaf14eg-1.jpg?height=268&width=394&top_left_y=1602&top_left_x=1368)
A2. C) 14 If Kevin draws $n$ lines, then the angle of $360^{\circ}$ at point $P$ is divided into $2 n$ pieces. If he were to draw 13 lines with equal angles between consecutive lines, then that angle would be exactly $\frac{1}{26} \cdot 360^{\circ}=13 \frac{11}{13}^{\circ}$. We see that 13 lines are not enough. If Kevin draws 14 lines with at least $13^{\circ}$ between consecutive lines, then the 28 angles together would be $28 \cdot 13^{\circ}=364^{\circ}$, which is impossible. With 14 lines, you can be sure that there is an angle of less than $13^{\circ}$.