1. The problem asks to find the supplement of an angle measuring 37°39'17". 2. The supplement of an angle is found using the formula: $$\text{Supplement} = 180^\circ - \text{angle}$$ 3. Convert the angle to decimal degrees for easier calculation: $$37^\circ + \frac{39}{60} + \frac{17}{3600} = 37 + 0.65 + 0.0047 = 37.6547^\circ$$ 4. Calculate the supplement: $$180^\circ - 37.6547^\circ = 142.3453^\circ$$ 5. Convert the decimal back to degrees, minutes, and seconds: - Degrees: 142° - Minutes: $0.3453 \times 60 = 20.718$ minutes - Seconds: $0.718 \times 60 = 43.08$ seconds 6. Final answer: The supplement is approximately 142°20'43".