# Can someone please explain how to do #17?  Thanks!

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This image has been Flagged as inappropriate Click to unflag Since m||n then we know that their are angle pairs that exist to make equality statements.

`/_3 and/_5` are known as either same-side interior angles or consecutive interior angles.  When lines are parallel, same-side interior angles together = 180˚.  This makes the equation:

`(6x + y) + (8x + 2y) = 180`

`14x + 3y = 180`

We also know that `/_5 and/_6`  form a linear pair which,  together, must equal 180˚. This makes the equation:

`(8x + 2y) + (4x + 7y) = 180`

`12x + 9y = 180`

Now that we have a system of equations, we can solve for x and y.  This case I will use the elimination method.

i.) 14x + 3y = 180

ii.) 12x + 9y = 180

Multiply equation (i.) by -3 to obtain the coefficient -9 which will be opposite of 9 in eqution ii.

`-3(14x + 3y=180) rArr -42x -9y = -540`

Add the new equation to equation ii.

` -42x - 9y = -540`

` 12x + 9y = 180 `

`-30x = -360`

`x = 12`

Substitute to find y.

`12(12) + 9y = 180 `

`144 + 9y = 180 `

`9y = 36 `

`y = 4`

x = 12 and y = 4

To find `/_7` , we know that `/_6 and/_7`  are equal because all vetical angles are equal.

Therefore,`/_6` is 4x + 7y = 4(12) + 7(4) = 48 + 28 = 76.

`/_7` is also 76˚

The solution for the given problem is x = 12, y = 4, and `/_7` = 76˚.

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