Question

Figure JKLM is a rectangle, so mAngleKJM = mAngleKLM = 90° and AngleKJC Is-congruent-toAngleMLC.

A rectangle has corner points J, K, L, M going clockwise. 2 lines are inscribed within the rectangle. One line goes from K to M, and the other line goes from J to L. Both lines intersect in the middle to form point C. All lines in the rectangle are the same length.
Which reason justifies the statement that AngleKLC is complementary to AngleKJC?

Angles that are congruent are complementary to the same angle.
Angles that are congruent are supplementary to the same angle.
All angles in a rectangle are right angles.
Complementary angles are always also c

Answer 1

Answer: The reason that justifies the statement that AngleKLC is complementary to AngleKJC is "Angles that are congruent are complementary to the same angle."

In the given scenario, AngleKJC and AngleMLC are congruent angles because they are opposite angles formed by the intersection of parallel lines. Since AngleKJC and AngleMLC are congruent, and in general, angles that are congruent are complementary to the same angle, we can conclude that AngleKLC is complementary to AngleKJC.

Complementary angles are pairs of angles that add up to 90 degrees. In this case, since AngleKJC and AngleMLC are congruent, they are both complementary to AngleKLC. This means that the sum of AngleKJC and AngleKLC is 90 degrees.

It's important to note that not all angles in a rectangle are right angles. In a rectangle, the only angles that are guaranteed to be right angles are the four corners of the rectangle. The reason we can say that AngleKJC and AngleMLC are congruent is because they are opposite angles formed by intersecting lines within the rectangle.

To summarize, the reason that justifies the statement that AngleKLC is complementary to AngleKJC is that angles that are congruent are complementary to the same angle. In this case, AngleKJC and AngleMLC are congruent angles, so they are both complementary to AngleKLC.