Question

Consider parallelogram VWXY below using information given in the figure to find x, m angle zvw and m angle zwv

Answer 1

ANSWERS

• x = 5

,

• m∠ZVW = 46°

,

• m∠ZWV = 41°

EXPLANATION

The diagonals of a parallelogram bisect each other, so

$11=5x+1$

To find x subtract 1 from both sides of the equation,

$\begin{gathered} 11-1=5x+1-1 \\ 10=5x \end{gathered}$

And divide both sides by 5,

$\begin{gathered} \frac{10}{5}=\frac{5x}{5} \\ 2=x \end{gathered}$

Hence x = 5

By the SAS property, triangle VZW and XZY are congruent:

Therefore, corresponding angles are also congruent. Angle ZXY is the one formed by the blue half-diagonal and the third side of the triangle, therefore its corresponding angle for the other triangle is the one formed also by the blue half-diagonal and the third side of the triangle, which is angle ZVW,

$\angle ZVW\cong\angle\text{ZXY}$$m\angle ZVW=46$

It is a similar situation for angle ZWV. This angle is formed by the light blue half-diagonal and the third side of triangle VZW, so its corresponding angle in triangle XZY is the one also formed by the light blue half-diagonal and the third side of the triangle, which is angle ZYX,

$\angle\text{ZWV}\cong\angle\text{ZYX}$$m\angle ZWV=41$