Which of the following is equivalent to the value of (5π9c+13π18c−17π6c) when converted to degrees? A 20∘ B 80∘ C 280∘ D 320∘

Question

Which of the following is equivalent to the value of (5π9c+13π18c−17π6c)  when converted to degrees?   A	20∘ B	80∘ C	280∘ D	320∘

Bytelearn · Accepted Answer

Convert to degrees: Convert each term in the expression from radians to degrees. To convert radians to degrees, we use the formula: degrees = radians * (180/π). Let's convert each term separately. For the first term, 5π/9c, we have: (5π/9c) * (180/π) = (5 * 180/9)c = (5 * 20)c = 100c degrees.Convert second term: Convert the second term, 13π/18c, to degrees. Using the same conversion formula: (13π/18c) * (180/π) = (13 * 180/18)c = (13 * 10)c = 130c degrees.Convert third term: Convert the third term, 17π/6c, to degrees. Again, using the conversion formula: (17π/6c) * (180/π) = (17 * 180/6)c = (17 * 30)c = 510c degrees.Combine converted terms: Combine the converted terms to find the total value in degrees. Now we add the first two terms and subtract the third term: 100c degrees + 130c degrees - 510c degrees. This simplifies to: (100 + 130 - 510)c degrees = (230 - 510)c degrees = -280c degrees. Since c is a common factor, it cancels out, leaving us with -280 degrees.Determine matching option: Determine which of the given options matches the calculated degree value. The calculated value is -280 degrees. However, the options are all positive degrees. We know that adding or subtracting full rotations (360 degrees) does not change the angle's position. Therefore, we can add 360 degrees to -280 degrees to find an equivalent positive angle. -280 degrees + 360 degrees = 80 degrees.Choose correct option: Choose the correct option that matches the calculated degree value. The correct option that matches 80 degrees is option B.

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

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