Question

Consider parallelogram VWXY below.Use the information given in the figure to find m ZZVW, x, and m ZZWV.3x + 3m ZZVm ZZW42064°X

Answer 1

Given :

`\begin{gathered} \angle ZYX=42^0 \\ \angle ZXY=64^0 \\ YZ\text{ = 6} \\ ZW\text{ = 3x + 3} \end{gathered}`

Required :

`\angle\text{ ZVW , x, }\angle\text{ ZWV}`

From the properties of a parallelogram,

The diagonals separate it into two congruent triangles. Hence,

`\Delta\text{ VYX }\cong\text{ }\Delta\text{ }VWX`

Remember that congruent triangles have the same three sides and exactly the same three angles

`\begin{gathered} \text{Hence ZY = ZW } \\ 6\text{ = 3x + 3} \\ \text{collect like terms} \\ 3x\text{ = 3} \\ x\text{ = 1} \end{gathered}`

Similarly,

`\begin{gathered} \angle ZVW=64^0 \\ \angle ZWV=42^0 \end{gathered}`

Note: The congruent triangles are flipped along the diagonal