Question

Please help! ^^ thank you!

Answer 1

Solving for x and y given the angles that are in terms of x and y

Answer:

`x = 16` and
`y = 20`

Explanation:

Angles
`(5x -16)^(\circ)` and
`(6y -4)^(\circ)` are supplementary. this means they should add up to
`180^(\circ)`. we can write the equation:
`(5x -16)^(\circ) +(6y -4)^(\circ) = 180^(\circ)`

Also, we can see that angles
`(6y -4)^(\circ)` and
`(7x +4)^(\circ)` are transversals. Transversal angles are equal. we can therefore write the equation:
`(6y -4)^(\circ) = (7x +4)^(\circ)`.

We now have the system of equations:

`\begin{cases} (5x -16)^(\circ) +(6y -4)^(\circ) = 180^(\circ) \\ (6y -4)^(\circ) = (7x +4)^(\circ) \end{cases}`

Let's solve for
`y` in terms of
`x` in this equation,
`(6y -4)^(\circ) = (7x +4)^(\circ)`, first.

`(6y -4)^(\circ) = (7x +4)^(\circ) \\ 6y -4 = 7x +4 \\ 6y = 7x +4 +4 \\ 6y = 7x +8 \\ y = (7x +8)/(6)`

Now let's solve for the equation
`(5x -16)^(\circ) +(6y -4)^(\circ) = 180^(\circ)` by plugging in
`y`.

`(5x -16)^(\circ) +(6y -4)^(\circ) = 180^(\circ) \\ 5x -16 +6y -4 = 180 \\ 5x +6y -20 = 180 \\ 5x +6((7x +8)/(6)) -20 = 180 \\ 5x +7x +8 -20 = 180 \\ 12x -12 = 180 \\ 12x = 180 +12 \\ 12x = 192 \\ x = (192)/(12) \\ x = 16`.

Now let's just solve for the equation,
`y = (7x +8)/(6)\\`, by plugging in the value of
`x`.

`y = (7(16) +8)/(6) \\ y = (112 +8)/(6) \\ y = (120)/(6) \\ y = 20`