Answer and Step-by-step explanation:
To solve, we need to understand what it means for an angle to be a complement of another angle.
Complement angles are those whose sum makes 90 degrees when added together, whether they are adjacent (right next to) or non-adjacent (not next to) each other.
If angle 1 is a complement of angle 4, that means that the sum of angle 1 and angle 4 is equal to 90 degrees.
Let's make an equation to solve for angle 4.
∠1 + ∠4 = 90°
Subtract ∠1 from both sides of the equation.
∠1 + ∠4 - ∠1 = 90° - ∠1
∠4 = 90° - ∠1
We can now substitute 33° for ∠1.
∠4 = 90° - 33°
∠4 = 57°
So, the measure of angle 4 ∠4 is 57°.