2. Using the degrees/minutes/seconds button on your calculator, write each of the following in degrees and minutes, give answers to the nearest minute. \( \begin{array}{ll}\text { a. } 17.8^{\circ} & \text { c. } 63.7^{\circ} \\ \text { b. } 48.52^{\circ} & \text { d. } 108.33^{\circ}\end{array} \)

To convert decimal degrees into degrees and minutes, we follow these steps: 1. The whole number part of the decimal represents the degrees. 2. The decimal part is multiplied by 60 to convert it into minutes. 3. Round the minutes to the nearest whole number. Let's perform these calculations for each of the given angles. ### a. \( 17.8^{\circ} \) 1. Degrees: \( 17 \) 2. Decimal part: \( 0.8 \) 3. Convert to minutes: \( 0.8 \times 60 = 48 \) Thus, \( 17.8^{\circ} = 17^{\circ} 48' \). ### b. \( 48.52^{\circ} \) 1. Degrees: \( 48 \) 2. Decimal part: \( 0.52 \) 3. Convert to minutes: \( 0.52 \times 60 = 31.2 \) (round to \( 31 \)) Thus, \( 48.52^{\circ} = 48^{\circ} 31' \). ### c. \( 63.7^{\circ} \) 1. Degrees: \( 63 \) 2. Decimal part: \( 0.7 \) 3. Convert to minutes: \( 0.7 \times 60 = 42 \) Thus, \( 63.7^{\circ} = 63^{\circ} 42' \). ### d. \( 108.33^{\circ} \) 1. Degrees: \( 108 \) 2. Decimal part: \( 0.33 \) 3. Convert to minutes: \( 0.33 \times 60 = 19.8 \) (round to \( 20 \)) Thus, \( 108.33^{\circ} = 108^{\circ} 20' \). ### Summary of Results: - a. \( 17.8^{\circ} = 17^{\circ} 48' \) - b. \( 48.52^{\circ} = 48^{\circ} 31' \) - c. \( 63.7^{\circ} = 63^{\circ} 42' \) - d. \( 108.33^{\circ} = 108^{\circ} 20' \)