Question

geometry (b)
parallel lines quick quiz
name: heaven jones
period:
in the diagram to the right, a || b.
1.) list one pair of corresponding angles.
2.) what name do we give the angle pair of ∠2 and ∠7?
3.) if m∠5 = 113.4°, what is m∠2?
4.) are ∠4 and ∠6 congruent or supplementary? briefly explain.

Explanation:

Step1: Recall corresponding - angles property

When \(a\parallel b\), corresponding angles are equal. For example, \(\angle1\) and \(\angle5\), \(\angle2\) and \(\angle6\), \(\angle3\) and \(\angle7\), \(\angle4\) and \(\angle8\) are pairs of corresponding angles. So for question 1, a correct pair is \(\angle1\) and \(\angle5\).

Step2: Identify angle - pair type

\(\angle2\) and \(\angle7\) are alternate exterior angles, not corresponding angles.

Step3: Use angle - relationship for parallel lines

Since \(a\parallel b\), \(\angle5\) and \(\angle2\) are alternate exterior angles. Alternate exterior angles are equal when two lines are parallel. So if \(m\angle5 = 113.4^{\circ}\), then \(m\angle2=113.4^{\circ}\).

Step4: Analyze \(\angle4\) and \(\angle6\)

\(\angle4\) and \(\angle6\) are same - side interior angles. Same - side interior angles are supplementary when two lines are parallel. That is, \(m\angle4 + m\angle6=180^{\circ}\).

Answer:

1. \(\angle1\) and \(\angle5\)
2. Alternate exterior angles
3. \(113.4^{\circ}\)
4. Supplementary. They are same - side interior angles for parallel lines \(a\) and \(b\), so \(m\angle4 + m\angle6 = 180^{\circ}\).