Nes and m are intersected by transversal t. ∥ m. Lines l and m are horizontal with l above m and intersected by transveral t. Angles 1, 2, 3, and 4 are formed where t intersects l with 1 and 3 above l from left to right and 2 and 4 below it. Angles 5, 6, 7, and 8 are formed where t intersects m with angles 5 and 7 above line m from left to right and 6 and 8 below it. Select all the angles that are supplementary to ∠4.

The supplementary angles to ∠4 are;

∠3, ∠2, ∠7, ∠6, and ∠5

Step-by-step explanation:

The given information are;

The angular orientation of lines l and m = horizontal lines

Therefore l and m are parallel lines

The transversal line to lines l and m = Line t

Therefore, we have;

Angles between line t and line l = 1, 2, 3, and 4

The order of arrangement of the angles between line t and line l are from top left in a clockwise order;

1, 3, 4, and 2

Similarly, the order of arrangement of the the angles between the transversal t and the line m are from top left in a clockwise order;

5, 7, 8, and 6

Therefore, we have;

The supplementary angles to ∠4 are;

∠3, ∠2, ∠7, ∠6, and ∠5

∠3 and ∠4, ∠4, and ∠2,  angles on a straight line between lines l and t

∠4 and ∠7 are opposite interior angles (Opposite interior angles are supplementary)

∠7 ≅ ∠6, ∠7 and ∠6 are alternate angles (

∠7 = ∠6 Definition of congruency

∴ ∠4 and ∠6 are supplementary (Transitive property)

∠4 and ∠5 are alternate interior angles (Alternate interior angles are supplementary).