Question

1. identify the three correct angles that are supplementary to ∠1. 9. classify each angle pair using the diagram. ∠1 and ∠5__ ∠4 and ∠5 ∠1 and ∠8 ∠3 and ∠4 ∠4 and ∠6__

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180 degrees. Adjacent angles that form a straight - line are supplementary. Also, when two parallel lines are cut by a transversal, same - side interior angles are supplementary.

Step2: Identify angles supplementary to ∠1

• ∠2: ∠1 and ∠2 are adjacent and form a straight - line, so ∠1+∠2 = 180°.
• ∠3: ∠1 and ∠3 are vertical angles' supplements. Since ∠1 and ∠4 are vertical angles, and ∠3+∠4 = 180°, ∠1 and ∠3 are supplementary.
• ∠7: ∠1 and ∠7 are same - side interior angles when the two horizontal lines are considered parallel and cut by the transversal, so ∠1+∠7 = 180°.

Step3: Classify angle pairs

• ∠1 and ∠5: Corresponding angles. They are in the same relative position with respect to the parallel lines and the transversal.
• ∠4 and ∠5: Alternate interior angles. They are between the two parallel lines and on opposite sides of the transversal.
• ∠1 and ∠8: Alternate exterior angles. They are outside the two parallel lines and on opposite sides of the transversal.
• ∠3 and ∠4: Adjacent angles. They share a common side and a common vertex.
• ∠4 and ∠6: Same - side interior angles. They are between the two parallel lines and on the same side of the transversal.

Answer:

1. The angles supplementary to ∠1 are ∠2, ∠3, ∠7.

9.
∠1 and ∠5: Corresponding angles
∠4 and ∠5: Alternate interior angles
∠1 and ∠8: Alternate exterior angles
∠3 and ∠4: Adjacent angles
∠4 and ∠6: Same - side interior angles