Question

consider parallelogram jklm below. use the information given in the figure to find m∠njk, m∠nkj, and x. m∠njk = □° m∠nkj = □° x = □

Explanation:

Step1: Find $\angle NJK$ (alternate interior angles)

In parallelogram $JKLM$, $JK \parallel ML$, so $\angle NJK = \angle JML = 44^\circ$

Step2: Find $\angle NKJ$ (alternate interior angles)

In parallelogram $JKLM$, $KL \parallel JM$, so $\angle NKJ = \angle KLM = 62^\circ$

Step3: Solve for $x$ (diagonals bisect each other)

Diagonals of a parallelogram bisect each other, so $5x - 3 = 12$
Add 3 to both sides: $5x = 12 + 3 = 15$
Divide by 5: $x = \frac{15}{5} = 3$

Answer:

$m\angle NJK = 44^\circ$
$m\angle NKJ = 62^\circ$
$x = 3$