Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Americans pronounce kangaroo as kang-guh-ROO (/ˌkæŋgəˈru/). In "kangaroo", the "a" vowel before NG shifts toward "ay" — sounding like "ay" as in "say", a distinctly American pattern — most prominent in Midwestern American English; other GenAm speakers may use a less raised vowel. This is called the Cat-Vowel Before NG, the kind of sound shift that makes everyday speech feel effortless. It comes out as KANG·guh·ROO. Stress falls on the third syllable — keep everything else short and quick. You'll hear it in sentences like "The kangaroo carries its joey in its pouch".
Record yourself saying "kangaroo" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 7 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Before NG, the vowel changes to sound more like the AY (/eɪ/) diphthong. The middle part of the tongue lifts toward the roof of the mouth, then the front part arches up.

Lift the back of your tongue to the soft palate. Lower your soft palate to let air flow through your nose.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "kangaroo", the "a" vowel before NG shifts toward "ay" — sounding like "ay" as in "say", a distinctly American pattern — most prominent in Midwestern American English; other GenAm speakers may use a less raised vowel. Vowel changes to sound like /eɪ/ ("ay" as in "say").
Stress falls on the third syllable, not the others. Stretch ROO — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.