Question

Find the value of x for which WXYZ must be a parallelogram.

Answer 1

Answer:

(D)$x=2$

Step-by-step explanation:

It is given that ∠Z≅∠X, m∠W=4x+20 and m∠Y=x+2.

Now, we know that to make WXYZ a parallelogram, using the property that the opposite angles of the parallelogram are equal in measure, therefore

$m{\angle}W=m{\angle}Y$

Substituting the given values, we have

$4x+20=x+26$

⇒$4x-x=26-20$

⇒$3x=6$

⇒$x=2$

Thus, for the value of x=2, WXYZ must be a parallelogram.

Hence, option (D) is correct.

Answer 2

Set angle W equal to angle Y
4x + 20 = x + 26
Solve
4x = x + 6
3x = 6
x = 2

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