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. partially visible option complementary angles are always also congruent partially visible.

Explanation:

1. Recall the properties of rectangles and complementary angles. In rectangle JKLM, \( \angle KJM = \angle KLM = 90^\circ \). We know \( \angle KJC \cong \angle MLC \).
2. Analyze the first option: "Angles that are congruent are complementary to the same angle." Let's see, since \( \angle KJM = 90^\circ \), in \( \triangle KJC \), \( \angle KJC + \angle KLC = 90^\circ \) (because \( \angle KJM \) is a right angle and the sum of angles in a triangle or the angles forming a right angle). Also, since \( \angle KJC \cong \angle MLC \), the logic of congruent angles being complementary to the same angle (here \( \angle KLC \) and the angle complementary to \( \angle MLC \) would relate, but more directly, since \( \angle KJC \) and \( \angle KLC \) add to 90° as part of the right angle, and \( \angle KJC \cong \angle MLC \), the first option makes sense.
3. The second option is about supplementary angles (sum to 180°), which is not relevant here as we are dealing with a right angle (sum to 90°).
4. The third option (about all angles in a triangle being right angles) is false, triangles have one right angle at most in a right triangle.
5. The fourth option (complementary angles are always congruent) is false, complementary angles just sum to 90°, they don't have to be congruent (e.g., 30° and 60° are complementary but not congruent).

Answer:

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