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