Question

given JM=27, ml=16, jl=46, nk=15, KLM= 48, JkM=78, MJL=22, find each missing value.

Answer 1

Answer:

KL = 27

JK = 16

MK = 30

NL = 23

m∠JKL = 132°

m∠KLJ = 22°

m∠KMJ = 54°

m∠KJL = 26°

Step-by-step explanation:

The given parameters of the quadrilateral JKLM are;

JM = 27, ML = 16, JL = 46, NK = 15, KLM = 48, JKM = 78, MJL = 22

Taking the sides as parallel, we have that quadrilateral JKLM is a parallelogram

Therefore;

KL = JM = 27

JK = ML = 16

m∠KLJ = m∠MJL = 22°

MN = NK = 15

MK = MN + NK = 15 + 15 = 30

NL = JL/2 = 46/2 = 23

m∠KJM = m∠KLM = 48°

m∠KJL = m∠KLM - m∠MJL = 48° - 22° = 26°

m∠KML = m∠JKM = 78°

m∠MKL = 180° - m∠KML - m∠KLM = 180° - 78° - 48° = 54°

m∠MKL = 54°

m∠JKL = m∠JKM + m∠MKL = 78° + 54° = 132°

m∠KMJ = m∠MKL = 54°

Answer 2

Applying the properties of a parallelogram, the missing values are:

KL = 27; JK = 16; MK = 30; NL = 23

m∠JKL = 132°; m∠KLJ = 22°; m∠KMJ = 54°; m∠KJL = 26°

What are the Properties of a Parallelogram?

• Diagonals bisects each other into equal parts.
• Parallelograms have two pairs of opposite sides that are parallel and congruent to each other.
• Angles opposite each other in a parallelogram are equal.
• Consecutive angles in a parallelogram are supplementary.

Applying the properties of a parallelogram, we will find the given measures as follows:

KL = JM  (congruent sides)

KL = 27

JK = ML (congruent sides)

JK = 16

MK = 2(NK)

Substitute

MK = 2(15)

MK = 30

NL = 1/2(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° = 54°

m∠KMJ = m∠MKL = 54°

m∠KMJ = 54°

m∠KJL = 48° - 22°

m∠KJL = 26°

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