solve for the following using the theorems/properties of a isosceles trapezoid.
ne = 13 m
if jn = 27 m, then oe = 27 m
if m∠jon = 55°, then m∠one = 55°, and m∠nej =

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# Explanation:
## Step1: Properties of Isosceles Trapezoid
In an isosceles trapezoid, non - parallel sides (legs) are equal. Here, $OJ$ and $NE$ are legs. Given $OJ = 13m$, so $NE=13m$ (by the property of isosceles trapezoid: legs of an isosceles trapezoid are congruent).
## Step2: Diagonals of Isosceles Trapezoid
The diagonals of an isosceles trapezoid are congruent. If $JN$ and $OE$ are diagonals ($JN = 27m$), then $OE = 27m$ (by the property of isosceles trapezoid: diagonals of an isosceles trapezoid are congruent).
## Step3: Angles in Isosceles Trapezoid
Since $OJ\parallel NE$ (bases of trapezoid), $\angle JON$ and $\angle ONE$ are alternate interior angles. So $m\angle ONE=m\angle JON = 55^{\circ}$ (alternate interior angles are congruent for parallel lines $OJ\parallel NE$ and transversal $ON$).
For $m\angle NEJ$, in isosceles trapezoid $OJNE$, $\angle OJE+\angle NEJ = 180^{\circ}$ (consecutive interior angles for $OJ\parallel NE$). Also, $\triangle OJE$ is isosceles (because $OJ = NE$ and $OJNE$ is isosceles trapezoid, so $\angle OJE=\angle NEJ$ is wrong. Wait, another approach:
Since $OJNE$ is isosceles trapezoid, $\angle OJE=\angle NEJ$ (base angles of isosceles trapezoid). And $\angle JON + \angle OJE= 90^{\circ}$ (right - angled at $O$ assumed from the figure's right - angle mark near $O$). But wait, no, actually, since $OJNE$ is isosceles trapezoid and $OJ\parallel NE$, and we know $\angle JON = 55^{\circ}$, and $OJ = NE$, $ON = ON$ (common side). $\triangle OJN\cong\triangle NEO$ (by SSS if $OJ = NE$, $JN=OE$, $ON = ON$). But better:
Since $OJ\parallel NE$, $\angle JOE+\angle NEJ = 180^{\circ}$ (consecutive interior angles). Also, in right - angled at $O$ (from the figure's right - angle symbol near $O$), assume $\angle JOE = 90^{\circ}$, no, wait, no, the right - angle is for the length marking. Wait, actually, using the property of isosceles trapezoid:
Since $OJNE$ is isosceles trapezoid, $\angle OJE=\angle NEJ$. And $\angle JON$ and $\angle ONE$ are $55^{\circ}$. Also, in $\triangle OJE$ (isosceles, $OJ = NE$), and $OJ\parallel NE$, the sum of angles in trapezoid:
$m\angle NEJ=125^{\circ}$ (because $\angle JON = 55^{\circ}$, and $OJ\parallel NE$, $\angle JOE+\angle NEJ = 180^{\circ}$, but actually, using the property that in isosceles trapezoid, base angles are equal. Wait, no, another way:
Since $OJ\parallel NE$, $\angle JON=\angle ONE = 55^{\circ}$ (alternate interior angles). And $\angle OJE+\angle NEJ = 180^{\circ}$ (consecutive interior angles). Also, $OJ = NE$, so $\triangle OJE$ and $\triangle NEJ$ (not exactly). Wait, using the fact that in isosceles trapezoid $OJNE$, $\angle OJE=\angle NEJ$ (base angles). And $\angle JON = 55^{\circ}$, and $OJ\perp$ (from the right - angle symbol for the length $OJ$'s measurement, assume $OJ$ is perpendicular to the height - like side). Wait, no, the right - angle is for the length $OJ$ (13m). Actually, using the property of isosceles trapezoid:
Since $OJ\parallel NE$, $\angle JON$ and $\angle ONE$ are alternate interior angles ($m\angle ONE = 55^{\circ}$). And $\angle NEJ=125^{\circ}$ (because $\angle JON$ and $\angle NEJ$ are supplementary as $OJ\parallel NE$ and $JE$ is a transversal: $m\angle NEJ=180 - 55=125^{\circ}$)

# Answer:
$NE = 13m$, $OE = 27m$, $m\angle ONE = 55^{\circ}$, $m\angle NEJ=125^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Properties of Isosceles Trapezoid

Step2: Diagonals of Isosceles Trapezoid

Step3: Angles in Isosceles Trapezoid

Answer: