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JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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If I understood you correctly you want to create dropdown list with following options:
and if someone select Other then new text field will appear where user will have possibility to enter some text that will represent different degree.
You can do that with using conditional logic to hide/show fields.
Inside of Form Builder you need to create Dropdown list and one text field. And then you need to add condition which will show your text field if Other option is selected from the Dropdown list.
To find out how to set up conditional logic you can read following article:
Also here is the test form I made:
If you want you can clone it.
Hope this will help. Let us know if you need further assistance.