Question

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

Answer 1

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

Angles that are congruent are complementary to the same angle