Find the complementary and supplementary angles.
\[
39^{\circ} 21^{\prime} 35^{\prime \prime}
\]
The complementary angle is
Answer
Final Answer: The complementary angle is \(\boxed{50^{\circ} 38^{\prime} 25^{\prime \prime}}\) and the supplementary angle is \(\boxed{140^{\circ} 38^{\prime} 25^{\prime \prime}}\).
Step 1 ：Given angle is \(39^{\circ} 21^{\prime} 35^{\prime \prime}\).
Step 2 ：Convert the given angle to seconds: \(39^{\circ} 21^{\prime} 35^{\prime \prime} = 141695^{\prime \prime}\).
Step 3 ：Convert 90 degrees to seconds: \(90^{\circ} = 324000^{\prime \prime}\).
Step 4 ：Subtract the given angle from 90 degrees to find the complementary angle: \(324000^{\prime \prime} - 141695^{\prime \prime} = 182305^{\prime \prime}\).
Step 5 ：Convert the complementary angle back to degrees, minutes, and seconds: \(182305^{\prime \prime} = 50^{\circ} 38^{\prime} 25^{\prime \prime}\).
Step 6 ：Convert 180 degrees to seconds: \(180^{\circ} = 648000^{\prime \prime}\).
Step 7 ：Subtract the given angle from 180 degrees to find the supplementary angle: \(648000^{\prime \prime} - 141695^{\prime \prime} = 506305^{\prime \prime}\).
Step 8 ：Convert the supplementary angle back to degrees, minutes, and seconds: \(506305^{\prime \prime} = 140^{\circ} 38^{\prime} 25^{\prime \prime}\).
Step 9 ：Final Answer: The complementary angle is \(\boxed{50^{\circ} 38^{\prime} 25^{\prime \prime}}\) and the supplementary angle is \(\boxed{140^{\circ} 38^{\prime} 25^{\prime \prime}}\).
