We're in a similar situation, we've tried the answers left by a previous team member, but they're apparently incorrect and when we tried to reset them we're the same insufficient information message.
We called dev support and our case was escalated, but they have been incredibly vague on how long we could expect it to be before the sr team even contacts us. At this point we've been waiting for nearly two weeks with no word on how to move past this issue.
This is becoming a big issue as we can't deploy neccessary app updates and fixes until we get this resolved.
same problem here
it is a very irritating new policy thatis going to lead to a lot of developers having to pay for a new developer account
when i click forgot my answers i get a popup asking me to... answer my secret question (that is the entire point why i want to reset them, i do not know my answers)
when i click back and click it again i get a message saying they can not reset my question
After taking call with Apple support team I found the way to resolve this issue. They have suggested below solution which works.
1. Create a new user in your existing Mac Machine and login into that.
2. Go to System Preferences -> iCloud.
3. Sign-in with your Apple ID which is asking to enable Two Factor Authentication.
4. After sign-in it will not ask you to enter answer of any security question, rather it will ask you to enter a phone number which you want to use for Two Factor Authentication.
5. Enter your phone number and choose the way you would like get the OTP (via Message or Call).
6. Enter the OTP and you are done.
Now you can login to any machine or browser with your enabled Two Factor Authentication phone number.