Question

exterior angle theorem
the sum of the remote interior angles is equal to the non - adjacent exterior angle.

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 relates remote interior angles and a non - adjacent exterior angle. The Triangle Sum Theorem is about the sum of angles in a triangle. The Definition of Vertical Angles is about angles opposite each other when two lines intersect.
• A linear pair is a pair of adjacent angles whose non - common sides are opposite rays. The sum of angles in a linear pair is \(180^{\circ}\). Since \(\angle3\) and \(\angle4\) are adjacent and their non - common sides form a straight line (a ray and its opposite ray), by the Definition of a Linear Pair, \(\angle3+\angle4 = 180^{\circ}\).

Answer:

Definition of a Linear Pair.