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Consider parallelogram VWXY below.
Use the information given in the figure to find m∠YXV, m∠Y, and x.

Consider parallelogram VWXY below Use the information given in the figure to find mYXV mY and x class=

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mhanifa

Answer:

  • 56°, 84°, 3 units

Step-by-step explanation:

Properties of a parallelogram

  • Two adjacent angles are supplementary
  • Opposite angles are congruent
  • Opposite sides are parallel and congruent

Use the properties to find the required parameters

1) Find m∠YXV

  • m∠YXV + m∠VXW + m∠VWX = 180°
  • m∠YXV + 40° + 84° = 180°
  • m∠YXV = 180° - 124°
  • m∠YXV = 56°

2) Find m∠Y

  • m∠Y = m∠W = 84°

3) Find x

  • 2x = 6
  • x = 6/2
  • x = 3
semsee45

Answer:

m∠YXV = 56°

m∠Y = 84°

x = 3

Step-by-step explanation:

Sum of interior angles of a triangle = 180°

⇒ m∠W + m∠WVX + m∠VXW = 180°

⇒ 84° + m∠WVX + 40° = 180°

⇒ m∠WVX = 56°

As VW ║ YX  and  YV ║ XW  then  m∠WVX = m∠YXV

So m∠YXV = 56°

In a parallelogram, opposite angles are congruent

⇒ m∠Y = m∠W

⇒ m∠Y = 84°

In a parallelogram, opposite sides lengths are congruent

⇒ VW = YX

⇒ 2x = 6

⇒ x = 6 ÷ 2

⇒ x = 3

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