Answer:
The supplementary angles to ∠4 are;
∠3, ∠2, ∠7, ∠6, and ∠5
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).