Question

Need done in 10 min!!! HURRY PLEASE THANKS

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

Compare congruent 90 degree angles (Complementary angles) to the same angle. 90 to a 90 if you draw that out is a square. if side by side then it makes a Supplementary angle or 180 degrees. all angles in a rectangle are right angles (Complementary angles). if you split a supplementary (180 degrees in half) then you have two congruent 90 degree angles. that's why they are always congruent

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

Angles that are congruent are complementary to the same angle