Question

Figure JKLM is a rectangle, so mKJM = mKLM = 90° and KJC MLC.Which reason justifies the statement that KLC is complementary to KJC?a. Angles that are congruent are complementary to the same angle.b. Angles that are congruent are supplementary to the same angle.c. All angles in a rectangle are right angles.d. Complementary angles are always also congruent.

Answer 1

a) Angles that are congruent are complementary to the same angle

Explanation:

Considering the figure attached:

Two angles are complementary if their sum is 90°

given that :

∠KJM = ∠KLM = 90° --- (1)

∠KJC ≅ ∠MLC

⇒ ∠KJC = ∠MLC ---- (2)

∠KJM = ∠KJC + ∠CJM

so by (1) above eq becomes

∠KJC + ∠CJM = 90° --- (3)

Similarly for ∠KLM

∠KLM = ∠KLC + ∠MLC

∠KLC + ∠MLC = 90° ---- (4)

Substitute (2) in (4)

∠KLC + ∠KJC = 90°

Which proves that ∠KLC and ∠KJC are complementary angles

So,

Angles that are congruent are complementary to the same angle