Question

1. given that ∠z = ∠x, m∠w = 5x - 4, and m∠y = 2x + 14, find the value of x for which wxyz must be a parallelogram.

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - angles are equal. Here, $\angle W$ and $\angle Y$ are opposite angles. So, $m\angle W=m\angle Y$.

Step2: Set up the equation

Set up the equation $5x - 4=2x + 14$.

Step3: Solve for x

Subtract $2x$ from both sides: $5x-2x - 4=2x-2x + 14$, which simplifies to $3x-4 = 14$. Then add 4 to both sides: $3x-4 + 4=14 + 4$, so $3x=18$. Divide both sides by 3: $\frac{3x}{3}=\frac{18}{3}$, and $x = 6$.

Answer:

6