How can I reset the answers of the security questions of my Apple ID?
The reset procedure for security questions is here: https://support.apple.com/kb/HT201485


https://iforgot.apple.com/


It's one of the things you are recommended to do if you think your AppleID is compromised.

Below are more details and screen shots from a while back, but the links above have current information as well as discussion on how to get support in person and newer developments like Two Factor Authentication and 
using another trusted device.



If you know your password to your Apple ID and have set up a second email address, you can reset your security questions by logging into the web site https://appleid.apple.com even if you can't answer the security questions that normally are required to make changes to the existing security questions.

Once you have logged in, click 'Password and Security'.  Then click/tap the link in the lower right that says Forgot your answers? Send reset security info email to m * * * *@monsters.edu



You will get an email with a link to reset not only the security questions and answers, but correct your birth date which can be used to verity your identity when you are calling Apple or trying to reset a password.



I have an Apple ID with a recovery email, so perhaps if you have not entered that second email, you might not be able to send the reset email and might need to contact Apple directly for help with your Apple ID. I know of people that have gotten things reset over the phone even after the Mat Honan incident where his account was compromised over the phone with Apple's assistance.