Question

1. given that ∠z≅∠x, m∠w = 4x + 20, and m∠y = x + 26, find the value of x for which wxyz must be a parallelogram.

15
27
9
2

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - angles are equal. So, $\angle W$ and $\angle Y$ are supplementary (since adjacent angles in a parallelogram are supplementary, and $\angle W+\angle Y = 180^{\circ}$).
$4x + 20+x + 26=180$

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side of the equation.
$(4x+x)+(20 + 26)=180$
$5x+46 = 180$

Step3: Isolate the variable term

Subtract 46 from both sides of the equation.
$5x=180 - 46$
$5x=134$
$x=\frac{134}{5}=26.8$ (This is wrong. Let's use the correct property: opposite angles are equal. Since $\angle W$ and $\angle Y$ are opposite angles in a parallelogram, $\angle W=\angle Y$)
$4x + 20=x + 26$

Step4: Solve for x

Subtract $x$ from both sides: $4x - x+20=x - x + 26$, which gives $3x+20 = 26$.
Then subtract 20 from both sides: $3x+20 - 20=26 - 20$, so $3x = 6$.
Divide both sides by 3: $x=\frac{6}{3}=2$.

Answer:

2