Question

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1 multiple choice 10 points in the figure shown at the right, lines l and m are parallel. what type of angles do the angle pair of ∠1 and ∠2 form? corresponding angles alternate interior vertical angles same - side exterior alternate exterior same - side interior linear pair

Explanation:

Step1: Recall angle pair definitions

A linear pair of angles is formed when two adjacent angles are supplementary (their sum is \(180^\circ\)) and they form a straight line.

Step2: Analyze \(\angle1\) and \(\angle2\)

\(\angle1\) and \(\angle2\) are adjacent (share a common side) and their non - common sides form a straight line (since they are on a straight line \(l\) intersected by the transversal). Also, \(\angle1+\angle2 = 180^\circ\) (they are supplementary).

• Corresponding angles: These are in the same relative position at each intersection. \(\angle1\) and \(\angle2\) do not fit this.
• Alternate interior angles: These are non - adjacent and on opposite sides of the transversal, inside the two parallel lines. \(\angle1\) and \(\angle2\) are not alternate interior angles.
• Vertical angles: These are opposite each other when two lines intersect. \(\angle1\) and \(\angle2\) are not vertical angles.
• Same - side exterior: These are on the same side of the transversal and outside the two parallel lines. \(\angle1\) and \(\angle2\) do not fit.
• Alternate exterior: These are on opposite sides of the transversal and outside the two parallel lines. \(\angle1\) and \(\angle2\) do not fit.
• Same - side interior: These are on the same side of the transversal and inside the two parallel lines. \(\angle1\) and \(\angle2\) do not fit.
• Linear pair: As we analyzed, \(\angle1\) and \(\angle2\) form a linear pair.

Answer:

Linear pair (the option with "Linear pair" text)