To solve this problem, follow these steps:
1. Understand the definition of complementary angles:
Complementary angles are two angles whose measures add up to [tex]$90^{\circ}$[/tex].
2. Set up the equation:
Let's denote the unknown angle by [tex]\( x \)[/tex].
3. Express the complementary angle:
Since the angles are complementary, the measure of the complementary angle is [tex]\( 90^{\circ} - x \)[/tex].
4. Formulate the relationship:
According to the problem, the given angle is [tex]$35^{\circ}$[/tex] less than its complementary angle. This can be written as:
[tex]\[
x = (90^{\circ} - x) - 35^{\circ}
\][/tex]
5. Solve the equation:
Simplify and solve the equation step-by-step:
[tex]\[
x = 90^{\circ} - x - 35^{\circ}
\][/tex]
Combine the constant terms on the right side:
[tex]\[
x = 55^{\circ} - x
\][/tex]
Add [tex]\( x \)[/tex] to both sides to get:
[tex]\[
2x = 55^{\circ}
\][/tex]
Divide both sides by 2 to find:
[tex]\[
x = 27.5^{\circ}
\][/tex]
Thus, the angle that is [tex]$35^{\circ}$[/tex] less than its complementary angle is:
[tex]\[
\boxed{27.5^{\circ}}
\][/tex]
