The given figure is a trapezoid $WXYZ$ with $WX = 7$ and $YZ = 7$. The angle $Z$ is given as $68^{\circ}$. We are asked to find the measure of angle $Y$.

1. Problem Description

The given figure is a trapezoid $WXYZ$ with $WX = 7$ and $YZ = 7$. The angle $Z$ is given as $68^{\circ}$. We are asked to find the measure of angle $Y$.

2. Solution Steps

Since $WXYZ$ is a trapezoid and $WX \parallel YZ$, we have that adjacent angles between parallel sides are supplementary.

Also, since the non-parallel sides have equal length, $WX = YZ = 7$, this is an isosceles trapezoid.

In an isosceles trapezoid, the base angles are equal.

Therefore, $\angle Z = \angle W = 68^{\circ}$.

Also, $\angle X = \angle Y$.

Since $WZ \parallel XY$, we have that consecutive interior angles are supplementary. Thus,

$\angle Y + \angle Z = 180^{\circ}$.

$\angle Y + 68^{\circ} = 180^{\circ}$

$\angle Y = 180^{\circ} - 68^{\circ}$

$\angle Y = 112^{\circ}$.

Alternatively, since it is an isosceles trapezoid, $\angle Z = \angle W$ and $\angle X = \angle Y$. Also, $\angle W + \angle X = 180^{\circ}$ and $\angle Y + \angle Z = 180^{\circ}$.

Since $\angle Z = 68^{\circ}$, we have $\angle Y + 68^{\circ} = 180^{\circ}$, which gives $\angle Y = 180^{\circ} - 68^{\circ} = 112^{\circ}$.

3. Final Answer

112