Question

∠1 is a complement of ∠4, and ( mangle 1 = 33^circ ). find ( mangle 4 ).
diagram of intersecting lines with angles 1,2,3,4
( mangle 4 = square^circ )

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles are two angles whose sum is \(90^\circ\). So, if \(\angle 1\) and \(\angle 4\) are complementary, then \(m\angle 1 + m\angle 4=90^\circ\).

Step2: Substitute the given value of \(m\angle 1\)

We know that \(m\angle 1 = 33^\circ\). Substituting this into the equation \(m\angle 1 + m\angle 4=90^\circ\), we get \(33^\circ+m\angle 4 = 90^\circ\).

Step3: Solve for \(m\angle 4\)

To find \(m\angle 4\), we subtract \(33^\circ\) from both sides of the equation. So, \(m\angle 4=90^\circ - 33^\circ\). Calculating the right - hand side, \(90 - 33 = 57\), so \(m\angle 4 = 57^\circ\).

Answer:

\(57\)