Given :
[tex]\begin{gathered} \angle ZYX=42^0 \\ \angle ZXY=64^0 \\ YZ\text{ = 6} \\ ZW\text{ = 3x + 3} \end{gathered}[/tex]
Required :
[tex]\angle\text{ ZVW , x, }\angle\text{ ZWV}[/tex]
From the properties of a parallelogram,
The diagonals separate it into two congruent triangles. Hence,
[tex]\Delta\text{ VYX }\cong\text{ }\Delta\text{ }VWX[/tex]
Remember that congruent triangles have the same three sides and exactly the same three angles
[tex]\begin{gathered} \text{Hence ZY = ZW } \\ 6\text{ = 3x + 3} \\ \text{collect like terms} \\ 3x\text{ = 3} \\ x\text{ = 1} \end{gathered}[/tex]
Similarly,
[tex]\begin{gathered} \angle ZVW=64^0 \\ \angle ZWV=42^0 \end{gathered}[/tex]
Note: The congruent triangles are flipped along the diagonal
