Touch the tip of your tongue to the roof of your mouth just behind your teeth. Add vocal cord vibration as you release.

Americans pronounce degrees as duh-GREEZ (/dəˈgriz/). Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "Did you say the temperature is thirteen degrees?" or "I need to preheat the oven to three hundred fifty degrees Fahrenheit" — more examples below.
Record yourself saying "degrees" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 6 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. Add vocal cord vibration, then release.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Pull the corners of your lips back slightly. Arch the middle-front of your tongue high toward the roof of the mouth.

Same position as S, but add vocal cord vibration. Feel the buzz.

Click any sentence to see the full breakdown — every link, every reduction, every flap-T.
The textbook way isn't wrong — it's just not how anyone actually says it.
Stress falls on the second syllable, not the others. Stretch GREEZ — 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.