Motivating problem link: https://leetcode.com/problems/maximum-number-of-visible-points/description/ Solution Link: https://usaco.guide/problems/lc-maximum-number-of-darts-inside-of-a-circular-dartboard/solution

I understand the diagrams they have drawn but I am confused about the sign handling and correctness. For one, in their first picture, I would think the entry angle is negative since the angle between PO and the x axis is negative, but this doesn't appear the be the case? It doesn't look like a very obtuse angle either, so I am confused on how this actually is working? Also, the picture is very different for point that are lower than point p, where their entry angle picture looks more like the exit angle picture even, like this one: https://cdn.discordapp.com/attachments/976232955028570122/1344006379483959366/IMG_0046.png?ex=67bf56fb&is=67be057b&hm=24959f29c8069fac10e653c9dba755c1ce849fa8e57e64434e651a225be39e6d&

Could someone provide some details about how this is actually working?