Question

Which reason justifies the statement that KLC is complementary to KJC?

Answer 1

Well the third and last option are not rational, since all angles are not right angles, and just because they are comp does not mean they are congruent.

Answer 2

we know that

m∠KJM=m∠KLM=$90$°

m∠KJC=m∠MLC -----> equation $1$

m∠KJM=m∠KJC+m∠CJM=$90$° -----> equation $2$

m∠KLM=m∠KLC+m∠MLC=$90$° -----> equation $3$

Substitute equation $1$ in equation $3$

So

m∠KLM=m∠KLC+[m∠KJC]=$90$°

angles ∠KLC and ∠KJC------> are complementary angles

therefore

the answer is

Angles that are congruent are complementary to the same angle