Consider parallelogram VWXY below.
2 answers:
Answer:
Step-by-step explanation:
<u>Properties of a parallelogram</u>
- Two adjacent angles are supplementary
- Opposite angles are congruent
- Opposite sides are parallel and congruent
Use the properties to find the required parameters
1) <u>Find m∠YXV</u>
- m∠YXV + m∠VXW + m∠VWX = 180°
- m∠YXV + 40° + 84° = 180°
- m∠YXV = 180° - 124°
- m∠YXV = 56°
2) <u>Find m∠Y</u>
3) <u>Find x</u>
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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