Question

the two figures are congruent. find the values of the unknown variables

x=
28

y=
36

z=
40

Explanation:

Step1: Use the property of congruent figures

Congruent figures have equal corresponding sides and angles.

Step2: Identify corresponding sides and angles

For side \(x\), it corresponds to the side of length \(28\) (assuming proper congruent - part matching). For side \(y\), it corresponds to the side of length \(14\) (error in original thought, correct based on congruence). For angle \(z\), it corresponds to the angle of \(71^{\circ}\) (error in original thought, correct based on congruence).

Wait, there is a mistake in the original problem's given answer. If the two trapezoids are congruent:

• Corresponding sides: If we assume the first trapezoid has side \(x\) and the second trapezoid has a side of length \(18\) (assuming proper congruent - part matching, maybe mis - labeled in the problem statement). But if we go by the property of congruent figures (all corresponding parts are equal):

Let's assume the first trapezoid has side \(z\) and the second trapezoid has a side of length \(14\) (if they are corresponding sides) and the first trapezoid has an angle of \(71^{\circ}\) which is equal to an angle in the second trapezoid. If the first trapezoid has side \(x\) and the second trapezoid has side \(18\) (assuming they are corresponding sides) and the first trapezoid has side \(y\) and the second trapezoid has side \(14\) (assuming they are corresponding sides)

Answer:

If we assume the correct correspondence: \(x = 18\), \(y=14\), \(z = 71^{\circ}\)

But if we go by the problem's initial (maybe mis - labeled) intention (assuming wrong correspondence in the problem's given answer area):
If \(x = 28\) (assuming a wrong correspondence), \(y = 14\) (correcting the original wrong \(36\) to the corresponding side length of \(14\) as per congruence), \(z=71^{\circ}\) (correcting the original wrong \(40\) to the corresponding angle of \(71^{\circ}\) as per congruence)