Question

Question 8: Math question 1

Answer 1

Finding m∠X ⤵️

`\sf \: m∠X = 97° \\ \tt[ Opposite \: angles \: of \: a \: parallelogram \: are \: equal]`

Finding the X in the side VW ⤵️

`\sf \: VW=YX \\ \tt \: [parallel \: sides \: are \: equal]`

`\sf \: 3x = 9`

`\sf \: x = 3`

Finding m∠XWY

`\bf \: 180 - 97 - 30 = m∠XWY`

`\bf \: 180 - 127 = m∠XWY`

`\bf \: m∠XWY = 53 \degree`

Answer 2

m∠X = 97°
x = 3
m∠XWY = 53°

Explanation:

m∠x is 97°, this is because the opposite angles in a parallelogram are congruent. The opposite angle of angle X is 97°, so angle x is 97°

The opposite sides of a parallelogram are congruent.

• 3x = 9
• x = 9/3
• x = 3

For angle XWY, we can solve for the missing angle in the triangle VYW:

• 180° - 97° - 30° = m∠VWY
• 180° - 127° = m∠VWY
• 53° = m∠VWY

Now, ∠VWY and ∠XWY are alternate interior angles

That means that the two angles are congruent

m∠XWY = 53°

-Chetan K