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The Inscribed Quadrilateral Theorem can be used to determine whether $JKLM$ is cyclic. According this theorem, the opposite angles of the quadrilateral need to be supplementary. Calculate the sum of opposite angles' measures and see if it is true.

	Pair $1$	Pair $2$
Opposite Angles	$\angle J$ and $\angle L$	$\angle K$ and $\angle M$
Sum	$99^{\circ }+74^{\circ }=173^{\circ }\times$	$105^{\circ }+82^{\circ }=187^{\circ }\times$

The sum of the angle measures in each pair is not equal to $180^{\circ }.$ Therefore, neither $\angle J$ and $\angle L$ nor $\angle K$ and $\angle M$ are supplementary. This finding implies that $JKLM$ is not a cyclic quadrilateral.

By observing the diagram, $\angle VXY$ and $\angle YXW$ can be recognized to form a linear pair, so they are supplementary angles. By substituting $84^{\circ }$ for $m\angle VXY$ and $a^{\circ }$ for $m\angle YXW$ into the equation, the value of $a$ can be calculated. The value of $a$ is $96.$ Next, notice that $\angle VXY$ is the exterior angle of $WXYZ,$ while $\angle WZY$ is the opposite interior angle. Therefore, these angles are congruent. The measure of $VXY$ is $84^{\circ }$ and the measure of $\angle WZY$ is $3b^{\circ }.$ By substituting these values and solving the equation, the value of $b$ can be found. Therefore, the value of $b$ is $28.$ Similarly, $\angle YZU$ and $\angle WXY$ are the exterior angle and the opposite interior angle, respectively. By the property mentioned earlier, these angles are congruent. The measure of $\angle YZU$ is $2c^{\circ }$ and the measure of $\angle WXY$ is $a^{\circ },$ which is equal to $96^{\circ }.$ This information can be used to determine the value of $c.$ The value of $c$ is $48.$