Question

Shipping cranes can be used to load cargo onto ships. In ▱ JKLM, JL = 165.8, J
m ∟ JML = 50° Find the measure of each part of the crane.
HW 1: Find JN.
HW 2: Find LM.
HW 3: Find m ∟ JKL.
HW 5: Find m ∟ KLM.
HW 6: Find m∟ MJK.

Answer 1

The shipping crane is an illustration of parallelogram.

The given parameters are:

• JL = 165.8
• JK = 110
• $\angle JML = 50^o$

The Side Lengths

(a) Length JN

Point N is at the midpoint of length segment JL.

So, we have:

$JN = \frac{JL}2$

$JN = \frac{165.8}2$

$JN = 82.9$

Hence, the value of length JN is 82.9

(b) Length LM

Side length LM is opposite length segment JK.

So, we have:

$LM = JK$ --- the opposite sides of parallelograms

$LM = 110$

Hence, the value of length LM is 82.9

(c) Length LN

Point N is at the midpoint of length segment JL.

So, we have:

$LN = JN$

$LN = 82.9$

Hence, the value of length LN is 82.9

The Angles

(d) Angle JKL

Angle JKL is opposite angle JML.

So, we have:

$\angle JKL = \angle JML$ --- the opposite angles of parallelograms

$\angle JKL = 50$

Hence, the value of angle JKL is 50 degrees

(e) Angle KLM

Angle KLM is adjacent angle JML.

So, we have:

$\angle KLM + \angle JML =180$ --- adjacent angles of parallelograms

This gives

$\angle KLM + 50 =180$

Subtract 50 from both sides

$\angle KLM =130$

Hence, the value of angle KLM is 130 degrees

(f) Angle MJK

Angle MJK is opposite angle KLM.

So, we have:

$\angle MJK = \angle KLM$ --- the opposite angles of parallelograms

$\angle MJK = 130$

Hence, the value of angle MJK is 130 degrees

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