Figure JKLM is a rectangle, so mAngleKJM = mAngleKLM = 90° and AngleKJC Is-congruent-toAngleMLC.

Question

A rectangle has corner points J, K, L, M going clockwise. 2 lines are inscribed within the rectangle. One line goes from K to M, and the other line goes from J to L. Both lines intersect in the middle to form point C. All lines in the rectangle are the same length.
Which reason justifies the statement that AngleKLC is complementary to AngleKJC?

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.

Answer 1

To justify the statement that angle KLC is complementary to angle KJC, we need to look at the relationships between the angles in the triangle formed by the rectangle and the inscribed lines.

Since angles KJC and KLC share a common vertex at point C inside the rectangle and angle KJM is 90°, we can note that:

1. Angle KJC is part of a right triangle formed with the right angle at J.
2. Angle KLC is also formed at the point C.

To justify that angle KLC is complementary to angle KJC, we can use the following reasoning:

Angles that are congruent are complementary to the same angle.

This is accurate because if angle KJC is congruent to angle MLC (as stated in your problem), and since angle MLC is also supplementary to angle KLC (as they form a linear pair along line JL), it follows that KLC and KJC must be complementary.

Hence, the correct explanation is:

Angles that are congruent are complementary to the same angle.