The following are the missing values;
- KL = 27
- JK = 16
- MK = 30
- NL = 23
- m∠JKL = 132°
- m∠KLJ = 22°
- m∠KMJ = 54°
- m∠KJL = 26°
What are the missing values?
KL = JM (congruent sides of parallelogram)
Then,
KL = 27
JK = ML (congruent sides of parallelogram)
Then,
JK = 16
MK = 2(NK)
Substitute the value of NK
MK = 2(15)
MK = 30
NL = 1/2(JL)
Substitute the value of JL
NL = 1/2(46)
NL = 23
m∠JKL = 180° - m∠KLM (supplementary angles)
m∠JKL = 180 - 48
m∠JKL = 132°
m∠KLJ = m∠MJL (congruent angles)
m∠KLJ = 22°
m∠KMJ = m∠MKL (congruent angles)
m∠MKL = 180° - 78° - 48°
m∠MKL= 54°
m∠KMJ = m∠MKL = 54° (Congruent angles)
m∠KMJ = 54°
m∠KJL = 48° - 22°
m∠KJL = 26°