IPA: /ˌdɪsɪnˈdʒɛnjuəsli/
KK: /dɪsɪnˈdʒɛnjuəsli/
In a way that is not sincere or honest, often pretending to be unaware of the truth.
She disingenuously claimed that she had no idea about the problem, even though she was involved.
Disingenuously → It is formed from "dis-" (meaning apart or away) and "ingenuous" (from Latin "ingenuus", meaning native or freeborn, but in modern usage implies honesty or straightforwardness). The prefix "dis-" negates the quality of being "ingenuous", thus the word means not being straightforward or honest.
Think of 'dis-' meaning 'not' and 'ingenuous' meaning 'honest' — so disingenuously means not being honest.