Question

1. in the diagram, ∠3 and ∠4 share a common side and form a straight line. if ( mangle3 + mangle4 = 180^circ ), which theorem or postulate explains this relationship?

2.
options:

• alternate interior angles theorem
• vertical angles theorem
• linear pair postulate
• corresponding angles postulate

Explanation:

• The Alternate Interior Angles Theorem relates to angles formed by parallel lines and a transversal, not supplementary adjacent angles.
• The Vertical Angles Theorem states vertical angles are equal, not about supplementary angles.
• The Linear Pair Postulate says that if two angles form a linear pair (share a common side and form a straight line), their measures sum to \(180^\circ\). Since \(\angle3\) and \(\angle4\) share a common side and form a straight line (and \(m\angle3 + m\angle4 = 180^\circ\)), this postulate applies.
• The Corresponding Angles Postulate relates to angles in the same position relative to parallel lines and a transversal, not supplementary adjacent angles.

Answer:

Linear Pair Postulate