Question

Find the value of y.
(12x + 9)
(8x + 11)º
(14y + 7)o

Answer 1

y = 7

Explanation:

First, find the value of x.

`(12x + 9) + (8x + 11) = 180` (linear pair)

Solve for x

`12x + 9 + 8x + 11 = 180`

Collect like terms

`12x + 8x + 9 + 11 = 180`

`20x + 20 = 180`

Subtract 20 from both sides

`20x + 20 - 20 = 180 - 20`

`20x = 160`

Divide both sides by 20

`(20x)/(20) = (160)/(20)`

`x = 8`

Thus,

`(12x + 9) = (14y + 7)` (vertical angles)

Plug in the value of x, and solve for y

`12(8) + 9 = 14y + 7`

`96 + 9 = 14y + 7`

`105 = 14y + 7`

Subtract 7 from each side

`105 - 7 = 14y + 7 - 7`

`98 = 14y`

Divide both sides by 14

`(98)/(14) = (14y)/(14)`

`7 = y`