Question

1. choose the best answer. which two angles form a linear pair of angles? __ and __ ∠abc ∠dbc ∠efg ∠gfh

Explanation:

Step1: Recall linear pair definition

A linear pair of angles are adjacent angles that form a straight line (sum to \(180^\circ\)), sharing a common side and vertex, with non - common sides being opposite rays.

Step2: Analyze each angle pair

• For \(\angle EFG\) and \(\angle GFH\): They share the common vertex \(F\) and the common side \(FG\). The non - common sides \(FE\) and \(FH\) are opposite rays (lie on a straight line when combined with \(FG\)), so they form a linear pair.
• \(\angle ABC\) and \(\angle DBC\): These two angles are adjacent and form a right angle (since \(\angle DBC\) is part of a right angle at \(B\) with the horizontal line), so they sum to \(90^\circ\), not a linear pair.
• \(\angle ABC\) and \(\angle EFG\) or \(\angle GFH\): No common vertex or side to form a linear pair.
• \(\angle DBC\) and \(\angle EFG\) or \(\angle GFH\): No common vertex or side to form a linear pair.

Answer:

\(\angle EFG\) and \(\angle GFH\)