Question

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.
All angles in a rectangle are right angles.
Complementary angles are always also congruent

Answer 1

Angles that are congruent are complementary to the same angle.

Explanation:

Answer 2

Angles that are congruent are complementary to the same angle

Explanation:

see that attached figure to better understand the problem

we know that

Two angles are complementary if their sum is equal to
`90\°`

`m<KJM=m<KLM=90\°`

`m<KJC=m<MLC` -----> equation A

`m<KJM=m<KJC+m<CJM`

so

`m<KJC+m<CJM=90\°` -----> equation B

`m<KLM=m<KLC+m<MLC`

so

`m<KLC+m<MLC=90\°` -----> equation C

Substitute equation A in equation C

So

`m<KLC+[m<KJC]=90\°`

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

therefore

the answer is

Angles that are congruent are complementary to the same angle