Question

figure jklm is a rectangle, so ( mangle kjm=mangle klm = 90^{circ} ) and ( angle kjccongangle mlc ). which reason justifies the statement that ( angle klc ) is complementary to ( angle 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:

Step1: Recall the property of complementary angles

Complementary angles add up to \(90^{\circ}\). In rectangle \(JKLM\), \(\angle KLM = 90^{\circ}\). So, \(\angle KLC+\angle MLC=90^{\circ}\).

Step2: Use the given congruent angles

Since \(\angle KJC\cong\angle MLC\) (given), we can substitute \(\angle MLC\) with \(\angle KJC\) in the equation \(\angle KLC+\angle MLC = 90^{\circ}\). We get \(\angle KLC+\angle KJC=90^{\circ}\). This is based on the principle that angles that are congruent (\(\angle KJC\) and \(\angle MLC\)) are complementary to the same angle (\(\angle KLC\) and the relationship with \(\angle MLC\) leading to the relationship with \(\angle KJC\)).

Answer:

Angles that are congruent are complementary to the same angle.