Question

1. which pair of angles are alternate interior angles of parallel lines e and f?

( a ^ { circ } ) and ( b ^ { circ } )
( b ^ { circ } ) and ( d ^ { circ } )
( a ^ { circ } ) and ( d ^ { circ } )

Explanation:

Step1: Recall alternate - interior angles definition

Alternate - interior angles are formed when a transversal intersects two parallel lines. They lie between the two parallel lines and on opposite sides of the transversal.

Step2: Analyze each option

• Option A (\(a^{\circ}\) and \(b^{\circ}\)):

\(a^{\circ}\) and \(b^{\circ}\) do not lie between the same pair of parallel lines (line \(e\) and \(f\)) with a common transversal.

• Option B (\(b^{\circ}\) and \(d^{\circ}\)):

\(b^{\circ}\) and \(d^{\circ}\) do not lie between the parallel lines \(e\) and \(f\) with a common transversal.

• Option C (\(a^{\circ}\) and \(d^{\circ}\)):

Lines \(e\) and \(f\) are parallel. The angles \(a^{\circ}\) and \(d^{\circ}\) lie between the parallel lines \(e\) and \(f\) and on opposite sides of the transversal (the non - parallel line that intersects them). So, \(a^{\circ}\) and \(d^{\circ}\) are alternate - interior angles.

Answer:

C. \(a^{\circ}\) and \(d^{\circ}\)