Question

lines m and n are cut by transversal l. which angle relationships are correct? check all that apply. ∠1 and ∠8 are alternate exterior angles. ∠4 and ∠6 are same side interior angles. ∠5 and ∠7 are vertical angles. ∠2 and ∠8 are corresponding angles. ∠3 and ∠6 are alternate interior angles.

Explanation:

1. For ∠1 and ∠8: Alternate exterior angles are on opposite sides of the transversal and outside the two lines. ∠1 is above line m, ∠8 is below line n, and they are on opposite sides of transversal l. So this is correct.
2. For ∠4 and ∠6: Same - side interior angles are on the same side of the transversal and between the two lines. ∠4 is between m and l, ∠6 is between n and l, but they are on opposite sides of l. So this is incorrect.
3. For ∠5 and ∠7: Vertical angles are opposite each other when two lines intersect. ∠5 and ∠7 are opposite each other when line l intersects line n. So this is correct.
4. For ∠2 and ∠8: Corresponding angles are in the same position relative to the transversal and the two lines. ∠2 is above m, ∠8 is below n, not the same position. So this is incorrect.
5. For ∠3 and ∠6: Alternate interior angles are on opposite sides of the transversal and between the two lines. ∠3 is between m and l, ∠6 is between n and l, and on opposite sides of l. So this is correct.

Answer:

• ∠1 and ∠8 are alternate exterior angles.
• ∠5 and ∠7 are vertical angles.
• ∠3 and ∠6 are alternate interior angles.