Question

Consider parallelogram VWXY below.

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

Answer 1

m∠YXV = 56°

m∠Y = 84°

x = 3

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

Answer 2

• 56°, 84°, 3 units

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