Kansas State University yearbooks are digitized and available through the Internet Archive.
Simply locate the Royal Purple for the year you think your relative attended K-State, then search the issue. If there are no results, try other years. If again, there are no results, contact Morse Special Collections at firstname.lastname@example.org. Your relative may have attended a different institution or have been enrolled in a short course or extension program.
To confirm dates and degrees, it is best to contact the Office of the Registrar, email@example.com.