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°

Step-by-step 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} (10)/(5)=(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`