\( \# 4 \) i \( \angle 3 \) is a supplement of \( \angle 4 \), and \( m \angle 3=148^{\circ} \). Find \( m \angle 4 \). \( m \angle 4=\square^{\circ} \)

To find \( m \angle 4 \), we use the fact that supplementary angles add up to \( 180^{\circ} \). Since \( m \angle 3 = 148^{\circ} \), we can calculate \( m \angle 4 \) using the equation: \[ m \angle 4 = 180^{\circ} - m \angle 3 \] Substituting in the value of \( m \angle 3 \): \[ m \angle 4 = 180^{\circ} - 148^{\circ} = 32^{\circ} \] So, \( m \angle 4 = 32^{\circ} \). For some historical context, ancient Greek mathematicians, especially Euclid, laid the groundwork for geometry and angle relations like these in his work "Elements". He meticulously developed the concepts of angles and their properties, which are fundamental in many areas of mathematics today. In real-world applications, understanding supplementary angles is essential in fields such as architecture and engineering. When designing structures, ensuring that angles meet at correct measurements helps in creating stable and aesthetically pleasing buildings and objects, making the knowledge of angles incredibly practical!