Question

Create an equation to solve for x then solve for x.

Answer 1

Equation:
`2(9x + 15 + 6x + 15) = 360`

x = 10°

∠U = 105°

∠V = 75°

Explanation:

Hello!

The sum of angles in a parallelogram is 360°. The opposite angles of a parallelogram are congruent.

Part A

Equation:
`2(9x + 15 + 6x + 15) = 360`

Solve

• 
  `2(9x + 15 + 6x + 15) = 360`
• 
  `9x + 15 + 6x + 15 = 180`
• 
  `15x + 30 = 180`
• 
  `15x = 150`
• 
  `x = 10`

The value of x is 10°.

Part B

To find the measures of each angle, simply plug in 10° for x in each equation.

∠U

• 
  `9x + 15`
• 
  `9(10) + 15`
• 
  `90 + 15`
• 
  `105`

Angle U is 105°.

∠V

• 
  `6x + 15`
• 
  `6(10) + 15`
• 
  `60+15`
• 
  `75`

Angle V is 75°.

Answer 2

Explanation:

In parallelogram adjacent angles are supplementary

∠U +∠V = 180

9x + 15 + 6x + 15 = 180

Combine like terms

9x + 6x + 15 + 15 = 180

15x + 30 = 180

Subtract 30 from both sides

15x = 180 - 30

15x = 150

Divide both sides by 15

x = 150/15

x = 10

∠U = 9x + 15

= 9*10 + 15

= 90 + 15

∠U = 105

∠V = 6x + 15

= 6*10 + 15

= 60 + 15

∠V = 75