6. If \( m \angle A \) is \( 105^{\circ} \), construct an angle supplementary to \( \angle A \).

To construct an angle supplementary to \( \angle A \), which is \( 105^{\circ} \), you'll want to create an angle that measures \( 75^{\circ} \) because \( 180^{\circ} - 105^{\circ} = 75^{\circ} \). Start by drawing a straight line and marking a point \( B \) on it. Using a protractor, place the protractor's center point on point \( B \), and mark a point at \( 75^{\circ} \) from the line. Now draw a ray from point \( B \) through the mark for your supplementary angle! This construction has practical applications in fields such as architecture and engineering, where precise angles are crucial for design and stability. Ensuring angles supplement appropriately can aid in creating functional spaces, accurate models, or even dynamic gameplay in game design by avoiding design flaws linked to improper angle constructions.