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Figure JKLM is a rectangle, so mKJM = mKLM = 90° and KJC MLC.


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.

Respuesta :

calculista

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 [tex]90\°[/tex]

[tex]m<KJM=m<KLM=90\°[/tex]

[tex]m<KJC=m<MLC[/tex] -----> equation A

[tex]m<KJM=m<KJC+m<CJM[/tex]

so

[tex]m<KJC+m<CJM=90\°[/tex] -----> equation B

[tex]m<KLM=m<KLC+m<MLC[/tex]

so

[tex]m<KLC+m<MLC=90\°[/tex] -----> equation C

Substitute equation A in equation C

So

[tex]m<KLC+[m<KJC]=90\°[/tex]

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

therefore

the answer is

Angles that are congruent are complementary to the same angle


Ver imagen calculista
ashishdwivedilVT

The statement "All angles in a rectangle are right angles",  justifies the statement that "KLC is complementary to KJC".

In the rectangle JKLM, each angle is 90°, so angles that are congruent are supplementary to each other.

In the attached diagram,

∠K =90°

So, the sum of angles KJL and KLJ = 180-∠K

∠ KJL or ∠KJC +∠ KLJ or ∠KJC  = 180-90 =90°

What are complementary angles?

When the sum of two angles is 90°, they are complementary angles to each other.

So ∠ KJC and ∠ KLC are complementary angles.

Therefore, the statement "All angles in a rectangle are right angles",  justifies the statement that "KLC is complementary to KJC".

To get more about rectangles visit:

https://brainly.com/question/21669902

Ver imagen ashishdwivedilVT