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:

1. Analyze each option:

• Option 1: Angles that are congruent are complementary to the same angle. Let's see, we know \( \angle KJC \cong \angle MLC \) and \( \angle KLM = 90^\circ \), so \( \angle KLC+\angle MLC = 90^\circ \). Since \( \angle KJC \cong \angle MLC \), we can substitute \( \angle MLC \) with \( \angle KJC \), getting \( \angle KLC+\angle KJC = 90^\circ \), which means they are complementary. This option makes sense.
• Option 2: The statement is about complementary, not supplementary, so this is wrong.
• Option 3: The fact that all angles in a rectangle are right angles is given, but it doesn't directly justify why \( \angle KLC \) and \( \angle KJC \) are complementary.
• Option 4: Complementary angles don't have to be congruent, so this is a false statement.

Answer:

Angles that are congruent are complementary to the same angle.