Could you please set up a security question and answer on the page you are directed to when accessing your account? It should take just a few seconds. After that, you should be able to access other Settings securely including the link to close account if you wish to do it.
When you click on your name in the upper right corner and navigate to your Settings, you should be able to see the link to close your account on the "Contact info" page. Are you able to use it to close your account?