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Which of the following is equivalent to the value of $(\frac{5\pi}{9}+\frac{13\pi}{18}-\frac{17\pi}{6})$ when converted to degrees? $\newline$ (A) $20^\circ$ $\newline$ (B) $80^\circ$ $\newline$ (C) $280^\circ$ $\newline$ (D) $320^\circ$

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Convert between radians and degrees

Full solution

Q. Which of the following is equivalent to the value of

(\frac{5\pi}{9}+\frac{13\pi}{18}-\frac{17\pi}{6})

when converted to degrees?

\newline

(A)

20^\circ

\newline

(B)

80^\circ

\newline

(C)

280^\circ

\newline

(D)

320^\circ

Convert to degrees: Convert each term in the expression to degrees separately. $\newline$ The conversion factor from radians to degrees is $180^\circ/\pi$ . We will apply this to each term in the expression.
Convert $5\pi/9$ : Convert the first term $5\pi/9$ to degrees. $\newline$ $(5\pi/9) \times (180°/\pi) = 5 \times 20° = 100°$
Convert $\frac{13\pi}{18}$ : Convert the second term $\frac{13\pi}{18}$ to degrees. $\newline$ \left(\frac{\(13\)\pi}{\(18\)}\right) \times \left(\frac{\(180\)°}{\pi}\right) = \(13 \times $10$ ° = $130$ °
Convert $-\frac{17\pi}{6}$ : Convert the third term $-\frac{17\pi}{6}$ to degrees. $\newline$ (-\frac{\(17\)\pi}{\(6\)}) \times (\frac{\(180\)°}{\pi}) = \(-17 \times $30$ ° = $-510$ °
Add converted values: Add the converted degree values from steps $2$ , $3$ , and $4$ . $\newline$ $100^\circ + 130^\circ - 510^\circ = 230^\circ - 510^\circ = -280^\circ$
Adjust negative result: Since the result is negative, we can add $360°$ to find the equivalent positive angle, if necessary. $\newline$ $-280° + 360° = 80°$
Choose correct option: Choose the correct option that matches the calculated degree value. $\newline$ The correct option is $80^\circ$ , which corresponds to option B.

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