Answer :

Answer :

  • x = 1
  • m∠ZVW = 61°
  • m∠ZWV = 43°

Solution :

1) x

the diagonals of a llgm bisect each other

thus,

  • ZY = ZW
  • 3 = 2x + 1
  • 3 -1 = 2x
  • 2 = 2x
  • x = 2/2
  • x = 1

2) m∠ZVW

  • m∠ZVW = m∠ZXY ( alternate interior angles )
  • m∠ZVW = 61°

3) m∠ZWY

  • m∠ZWV = m∠ZYX ( alternate interior angles )
  • m∠ZWV = 43°

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]