Question

module 3 lesson 3-7 quiz
name:
angles\tname of angle pair\trelationship (congruent or supplementary)

1. ∠3 and ∠6\talternate interior angles\t
2. ∠1 and ∠5\tcorresponding angles\t
3. ∠6 and ∠8\t\t
4. ∠2 and ∠7\t\t
5. ∠3 and ∠5\t\t
6. ∠2 and ∠3\t\t

1. if angles 4 is 50 degrees what is the measure of angle 5?
2. if angles 4 is 50 degrees what is the measure of angle 6?

Explanation:

Step1: Recall angle - pair relationships

• Alternate interior angles: If two parallel lines are cut by a transversal, alternate interior angles are congruent. For example, \(\angle3\) and \(\angle6\) are alternate interior angles, so they are congruent.
• Corresponding angles: If two parallel lines are cut by a transversal, corresponding angles are congruent. \(\angle1\) and \(\angle5\) are corresponding angles, so they are congruent.
• Vertical angles: Vertical angles are congruent. \(\angle6\) and \(\angle8\) are vertical angles. So the name of the angle - pair is “Vertical angles” and their relationship is “Congruent”.
• Alternate exterior angles: \(\angle2\) and \(\angle7\) are alternate exterior angles. If two parallel lines are cut by a transversal, alternate exterior angles are congruent. So the name of the angle - pair is “Alternate exterior angles” and their relationship is “Congruent”.
• Consecutive interior angles (same - side interior angles): \(\angle3\) and \(\angle5\) are consecutive interior angles. If two parallel lines are cut by a transversal, consecutive interior angles are supplementary. So the name of the angle - pair is “Consecutive interior angles” and their relationship is “Supplementary”.
• Adjacent angles (linear pair): \(\angle2\) and \(\angle3\) form a linear pair. A linear pair of angles is supplementary. So the name of the angle - pair is “Linear pair” and their relationship is “Supplementary”.

Step2: Use angle - pair relationships for angle measures

• For \(\angle4 = 50^{\circ}\) and \(\angle5\):
• \(\angle4\) and \(\angle5\) are consecutive interior angles. If two parallel lines are cut by a transversal, \(m\angle4+m\angle5 = 180^{\circ}\) (consecutive interior angles are supplementary).
• Given \(m\angle4 = 50^{\circ}\), then \(m\angle5=180 - 50=130^{\circ}\).
• For \(\angle4 = 50^{\circ}\) and \(\angle6\):
• \(\angle4\) and \(\angle6\) are alternate interior angles. If two parallel lines are cut by a transversal, alternate interior angles are congruent. So \(m\angle6=m\angle4 = 50^{\circ}\).

Answer:

1. Relationship: Congruent
2. Relationship: Congruent
3. Name of Angle Pair: Vertical angles; Relationship: Congruent
4. Name of Angle Pair: Alternate exterior angles; Relationship: Congruent
5. Name of Angle Pair: Consecutive interior angles; Relationship: Supplementary
6. Name of Angle Pair: Linear pair; Relationship: Supplementary
7. \(130^{\circ}\)
8. \(50^{\circ}\)