Convert the angle theta=(8pi)/(9) radians to degrees. Express your answer exactly. theta=◻^(@)

Convert to degrees: To convert radians to degrees, we use the conversion factor that pi radians is equal to 180 degrees. The formula to convert an angle in radians to degrees is: degrees = radians * (180/pi).Apply formula: Now, we apply the formula to theta=(8pi)/(9) radians. We multiply (8pi)/(9) by (180/pi) to convert it to degrees.Cancel out pi: The pi in the numerator and the pi in the denominator cancel out, leaving us with (8/9) * 180.Calculate exact value: We calculate (8/9) * 180 to get the exact value in degrees. (8/9) * 180 = 160 degrees.

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Convert the angle
theta=(8pi)/(9) radians to degrees.
Express your answer exactly.

theta=◻^(@)

Convert the angle $\theta=\frac{8 \pi}{9}$ radians to degrees. $\newline$ Express your answer exactly. $\newline$ $\theta=\square^{\circ}$

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Full solution

Q. Convert the angle

\theta=\frac{8 \pi}{9}

radians to degrees.

\newline

Express your answer exactly.

\newline

\theta=\square^{\circ}

Convert to degrees: To convert radians to degrees, we use the conversion factor that $\pi$ radians is equal to $180$ degrees. The formula to convert an angle in radians to degrees is: $\text{degrees} = \text{radians} \times (180/\pi)$ .
Apply formula: Now, we apply the formula to $\theta=\frac{8\pi}{9}$ radians. We multiply $\frac{8\pi}{9}$ by $\frac{180}{\pi}$ to convert it to degrees.
Cancel out pi: The $\pi$ in the numerator and the $\pi$ in the denominator cancel out, leaving us with $(\frac{8}{9}) \times 180$ .
Calculate exact value: We calculate $(\frac{8}{9}) \times 180$ to get the exact value in degrees. $(\frac{8}{9}) \times 180 = 160$ degrees.