Find the measure of the complement and the supplement of $35^{\circ}$. What is the measure of the complement of $35^{\circ}$ ?

Step 1 ：Define the given angle as \(35^{\circ}\).

Step 2 ：The complement of an angle is defined as \(90^{\circ}\) minus the angle.

Step 3 ：Subtract the given angle from \(90^{\circ}\) to find the complement.

Step 4 ：The complement of \(35^{\circ}\) is \(90^{\circ} - 35^{\circ} = 55^{\circ}\).

Step 5 ：Final Answer: The measure of the complement of \(35^{\circ}\) is \(\boxed{55^{\circ}}\).