Question

Find the value of x and y

Answer 1

`(6x+9)^o\ and\ 129^o\ are\ the\ vertical\ angles.\\\\\text{The vertical angles have the same measure. Therefore we have the equation:}\\\\6x+9=129\qquad\text{subtract 9 from both sides}\\\\6x=120\qquad\text{divide both sides by 6}\\\\\boxed{x=20}`

`3y^o\ and\ 129^o\ are\ the\ supplementary\ angles.\text{}\\\\\text{Supplementary angles are two angles with a sum of }\ 180^o.\\\text{Therefore we have the equation.}\\\\3y+129=180\qquad\text{subtract 129 from both sides}\\\\3y=51\qquad\text{divide both sides by 3}\\\\\boxed{y=17}\\\\Answer:\ \boxed{x=20^o\ and\ y=17^o}`

Answer 2

x=30

y=17

Explanation:

We know that 6x+9 = 129 since they are vertical angles

6x+9 = 129

Subtract 9 from each side

6x+9 -9 =129-9

6x = 120

Divide by 6

6x/6 =120/6

x = 20

3y+129 =180 since they make a straight line and straight line are equal to 180 degrees

3y+129 =180

Subtract 129 from each side

3y+129-129=180-129

3y = 51

Divide by 3

3y/3 = 51/3

y = 17