Answer:
x = 1
m∠ZVW = 61°
m∠ZWV = 43°
Step-by-step explanation:
In a parallelogram, the diagonals bisect each other. Therefore, as diagonals VX and WY of parallelogram VWXY bisect each other at point Z:
[tex]WZ = ZY\\\\2x + 1 = 3\\\\2x + 1 - 1 = 3 - 1\\\\2x = 2\\\\x = 1[/tex]
So, the value of x is:
[tex]\Large\boxed{\boxed{x = 1}}[/tex]
According to the Alternate Interior Angles Theorem, if two parallel lines are intersected by a transversal, the pairs of alternate interior angles formed on opposite sides of the transversal are congruent.
In this case, diagonal VX is a transversal intersecting parallel sides VW and XY, so angles ZVW and ZXY are the alternate interior angles and are therefore congruent. Given that angle ZXY measures 61°, it follows that:
[tex]\Large\boxed{\boxed{m\angle ZVW = 61^{\circ}}}[/tex]
Similarly, diagonal WY is also a transversal intersecting parallel sides VW and XY, so angles ZWV and ZYX are the alternate interior angles and are therefore congruent. Given that angle ZYX measures 43°, it follows that:
[tex]\Large\boxed{\boxed{m\angle ZWV = 43^{\circ}}}[/tex]
