Question

1. identify the angles that are congruent to ∠6. 4. identify the angles that are congruent to ∠3. 5. identify the angles that are supplementary to ∠3. 6. identify the angle that is vertical to ∠8.

Explanation:

Step1: Recall angle - relationship definitions

Supplementary angles add up to 180 degrees, congruent angles have the same measure, and vertical angles are opposite each other when two lines intersect.

Step2: Analyze supplementary angles to ∠3

If two angles are on a straight - line with ∠3, they are supplementary to ∠3. Assuming a set of parallel lines and a transversal, the angles that are supplementary to ∠3 are the ones that form a linear pair with it. Let's assume the standard angle - naming convention for parallel lines and a transversal. If ∠3 and ∠4 form a linear pair, ∠4 is supplementary to ∠3. Also, if we consider the corresponding and alternate - interior/exterior relationships, the angle that is supplementary to ∠3 (assuming a straight - line situation) could be another angle. But without a specific diagram showing parallel lines and a transversal, if we assume a basic linear - pair situation, if ∠3 and ∠4 are adjacent and on a straight line, ∠4 is supplementary. If we consider the full 180 - degree relationship around a point on the transversal, the angle that is supplementary to ∠3 is ∠4.

Step3: Analyze congruent angles to ∠6

Vertical angles to ∠6 are congruent to ∠6. Also, if we have parallel lines and a transversal, corresponding angles and alternate - interior/exterior angles to ∠6 are congruent. If ∠6 and ∠8 are vertical angles, ∠8 is congruent to ∠6. Also, if we assume parallel lines and a transversal, the corresponding angle to ∠6 (let's say in the same relative position on the other parallel line) is congruent, and the alternate - exterior angle (if applicable) is congruent.

Step4: Analyze vertical angle to ∠8

Vertical angles are opposite each other when two lines intersect. If ∠8 and ∠6 are vertical angles, then ∠6 is the vertical angle to ∠8.

3.

Answer:

• Supplementary to ∠3: ∠4
• Congruent to ∠6: ∠8
• Vertical to ∠8: ∠6