Question

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

Answer 1

Explanation:

A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. We know that for any parallelogram opposite angles are also equal. Here:

$\angle Z=\angle X \\ \\ \text{and this also must be true} \\ \\ \\ \angle W= \angle Y \\ \\ \\ Then: \\ \\ 4x + 20 = x + 26 \\ \\ \\ Solving \ for \ x: \\ \\ 4x-x=26-20 \\ \\ 3x=6 \\ \\ \boxed{x=2}$