Question

2025 nshs parallel lines and angles assessment
if ( a parallel b ) and ( m angle 1 = 138 ), what is ( m angle 5 )?
( 138 ^ { circ } )
( 132 ^ { circ } )
( 48 ^ { circ } )
( 42 ^ { circ } )

Explanation:

Step1: Find the measure of ∠3

∠1 and ∠3 are vertical angles. Vertical angles are equal. But wait, no! Wait, ∠1 and ∠3 are actually adjacent and form a linear pair. So \(m\angle1 + m\angle3=180^{\circ}\) (linear - pair postulate). Given \(m\angle1 = 138^{\circ}\), then \(m\angle3=180 - 138=42^{\circ}\).

Step2: Use the property of parallel lines

Since \(a\parallel b\) and \(t\) is a transversal, ∠3 and ∠5 are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(m\angle5=m\angle3\).

Answer:

\(42^{\circ}\)