Question

1. why is

\\( \angle 3+\angle 4=180^{\circ} \\) ?
the exterior angle
theorem
the triangle sum
theorem
definition of a linear
pair
definition of vertical
angles

Explanation:

• The Exterior Angle Theorem states that the sum of the remote interior angles equals the non - adjacent exterior angle (e.g., \(m\angle A + m\angle C=m\angle CBD\)), which is not related to \(\angle3+\angle4 = 180^{\circ}\).
• The Triangle Sum Theorem states that the sum of the interior angles of a triangle is \(180^{\circ}\) (\(m\angle1 + m\angle2 + m\angle3=180^{\circ}\)), not relevant to \(\angle3+\angle4 = 180^{\circ}\).
• Vertical angles are pairs of opposite angles formed by two intersecting lines and are equal, not related to \(\angle3+\angle4 = 180^{\circ}\).
• A linear pair of angles is formed when two adjacent angles form a straight line. By the definition of a linear pair, the sum of the measures of angles in a linear pair is \(180^{\circ}\). Since \(\angle3\) and \(\angle4\) form a linear pair (they are adjacent and their non - common sides form a straight line), \(\angle3+\angle4 = 180^{\circ}\) by the definition of a linear pair.

Answer:

Definition of a Linear Pair