Question

figure jklm is a rectangle, so m∠kjm = m∠klm = 90° and ∠kjc ≅ ∠mlc which reason justifies the statement that ∠klc is complementary to ∠kjc? 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

Explanation:

Since \(m\angle KJM = 90^{\circ}\), \(\angle KJC+\angle KLC = 90^{\circ}\) (because \(\angle KJM\) is composed of \(\angle KJC\) and \(\angle KLC\) in the right - angled context of the rectangle). Given \(\angle KJC\cong\angle MLC\), by the property that if two angles (\(\angle KJC\) and \(\angle MLC\)) are congruent and they are related to another angle (\(\angle KLC\)) such that one of the congruent angles (\(\angle KJC\)) and \(\angle KLC\) sum to \(90^{\circ}\) (complementary), the other congruent angle (\(\angle MLC\)) would also follow the same complementary relationship. The key theory here is the angle - congruence and complementarity relationship.

Answer:

Angles that are congruent are complementary to the same angle