Question

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

Answer 1

Answer:

Angles that are congruent are complementary to the same angle

Step-by-step 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