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 congruent.

Answer 1

"Angles that are congruent are complementary to the same angle."

Reason: ∠KLC + ∠MLC = 90° because ∠KLM is a right angle. Since ∠KJC ≅ ∠MLC, replacing ∠MLC with ∠KJC gives ∠KLC + ∠KJC = 90°, so ∠KLC is complementary to ∠KJC.