From a Kappy post
The Three Best Alternatives for Security Questions and Rescue Mail
1. Use Apple's Express Lane.
Go to https://expresslane.apple.com ; click 'See all products and services' at the
bottom of the page. In the next page click 'More Products and Services, then
'Apple ID'. In the next page select 'Other Apple ID Topics' then 'Forgotten Apple
ID security questions' and click 'Continue'. Please be patient waiting for the return
phone call. It will come in time depending on how heavily the servers are being hit.
2. Call Apple Support in your country: Customer Service: Contact Apple support.
A substitute for using the security questions is to use 2-step verification: