Question

figure j k l m is a rectangle, so ( m angle k j m = m angle k l m = 90 ^ { circ } ) and ( angle k j c cong angle m l c ). which reason justifies the statement that ( angle k l c ) is complementary to ( angle k j c )? 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 \(m\angle KLM = 90^{\circ}\), in \(\triangle KLC\), \(\angle KLC+\angle MLC = 90^{\circ}\) (because the sum of angles in a right - angled triangle's non - right angles is \(90^{\circ}\)).
• Given \(\angle KJC\cong\angle MLC\), we can substitute \(\angle MLC\) with \(\angle KJC\) in the equation \(\angle KLC+\angle MLC = 90^{\circ}\).
• The property "Angles that are congruent are complementary to the same angle" allows us to make this substitution. Angles \(\angle KLC\) and \(\angle MLC\) are complementary (\(\angle KLC+\angle MLC=90^{\circ}\)), and since \(\angle KJC\cong\angle MLC\), \(\angle KLC\) and \(\angle KJC\) are also complementary.

Answer:

Angles that are congruent are complementary to the same angle.