Which reason justifies the statement that KLC is complementary to KJC?
Which reason justifies the statement that KLC is complementary to KJC?
Well the third and last option are not rational, since all angles are not right angles, and just because they are comp does not mean they are congruent.
we know that
m∠KJM=m∠KLM=\(90\)°
m∠KJC=m∠MLC -----> equation \(1\)
m∠KJM=m∠KJC+m∠CJM=\(90\)° -----> equation \(2\)
m∠KLM=m∠KLC+m∠MLC=\(90\)° -----> equation \(3\)
Substitute equation \(1\) in equation \(3\)
So
m∠KLM=m∠KLC+[m∠KJC]=\(90\)°
angles ∠KLC and ∠KJC------> are complementary angles
therefore
the answer is
Angles that are congruent are complementary to the same angle