Question

Two lines intersect to form ∠ABC. One step in constructing a line parallel toBC through point A is to construct an angle with vertex A. How should this angle be related to ∠ABC?

A) The angles should be supplementary.
B) The angles should be congruent.
C) The angles should be complementary.
D) The angles should be vertical.

Answer 1

b. It's b because I know it's b.

Answer 2

When constructing a line parallel to BC through point A, the angle constructed with vertex A should be complementary to angle ABC.

Step-by-step explanation:

When constructing a line parallel to BC through point A, one step is to construct an angle with vertex A. This angle should be complementary to angle ABC.

To understand why, consider that when two lines are parallel, the corresponding angles formed by a transversal (the line that intersects the parallel lines) are congruent. In this case, angle ABC and the angle constructed with vertex A are corresponding angles, so they should be congruent. Since corresponding angles are congruent, they must add up to 180°, making them complementary angles.

So, the correct answer is C) The angles should be complementary.