Sometimes there is no 'Close Button' to close patch notes. 

1. Open the Launcher
2. Go to the Minecraft section, the Minecraft Dungeons section, or the What's New in the Launcher
3. Go to Patch Notes
4. Open a Patch Note

  There is no longer an X to close the Patch Note

When the close button does not appear, you need to press esc. This is not ideal as it sometimes requires you to press esc multiple times, and this does not always work; meaning you sometimes need to quit the launcher and re-open it.