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